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Michael drives x miles due north at arrives at Point A. He then heads

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Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.
[Reveal] Spoiler: OA

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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 27 Jul 2017, 23:39
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jedit wrote:
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.


Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13.

So total distance travelled by him must be 5+12+13 = 30 miles
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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 26 Aug 2017, 22:01
VeritasPrepKarishma wrote:
jedit wrote:
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.


Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13.

Hi is there any alternative way to solve this question ?
If No, is it advisable to learn the pythagorean triplets ? But there are so many triplets possible.
How is one supposed to solve it under 2 min ?


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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 26 Aug 2017, 23:44
jedit wrote:
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.



How do we know that triplet will be like that?

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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 27 Aug 2017, 02:31
can you please explain how you got 12 and 13 for other 2 sides?

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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 27 Aug 2017, 08:02
RashmiT wrote:
can you please explain how you got 12 and 13 for other 2 sides?


Hi RashmiiT,

Pythogoras triplet - 3:4:5. So we know shortest cannot be hypotenuse.

We have x^2 + 5^2 = z^2.

All 3 are integers. By testing various values for x we see that (12)^2 + (5)^2 = (13)^2.

So total distance is 12+ 5+ 13= 30

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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 27 Aug 2017, 08:39
VeritasPrepKarishma wrote:
jedit wrote:
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.


Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13.

So total distance travelled by him must be 5+12+13 = 30 miles


Hi VeritasPrepKarishma , I answered it 12 miles because I think "THE SHORTEST LEG" is the hypotenuse from the starting point to the last destination.

How must we translate this kind of word question?
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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 27 Aug 2017, 09:27
septwibowo wrote:
VeritasPrepKarishma wrote:
jedit wrote:
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.


Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13.

So total distance travelled by him must be 5+12+13 = 30 miles


Hi VeritasPrepKarishma , I answered it 12 miles because I think "THE SHORTEST LEG" is the hypotenuse from the starting point to the last destination.

How must we translate this kind of word question?



Hypotenuse is always the longest side in a RIGHT TRIANGLE

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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 27 Aug 2017, 10:00
rocko911 wrote:
septwibowo wrote:
VeritasPrepKarishma wrote:
[quote="jedit"]Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.


Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13.

So total distance travelled by him must be 5+12+13 = 30 miles


Hi VeritasPrepKarishma , I answered it 12 miles because I think "THE SHORTEST LEG" is the hypotenuse from the starting point to the last destination.

How must we translate this kind of word question?



Hypotenuse is always the longest side in a RIGHT TRIANGLE[/quote]

Sure, I understand that hypotenuse is the longest side of the triangle. But, we often face similar problem who assume the hypotenuse as a shortcut - so although that is the longest side, we can go from start to finish via hypotenuse rather than via its legs.


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Re: Michael drives x miles due north at arrives at Point A. He then heads [#permalink]

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New post 27 Aug 2017, 10:10
rocko911 wrote:
septwibowo wrote:
jedit wrote:
Michael drives x miles due north at arrives at Point A. He then heads due east for y miles. Finally, he drives z miles in a straight line until he reaches his starting point. If x, y, and z are integers, then how many miles did Michael drive if the shortest leg was 5 miles?

A - 5 miles

B - 12 miles

C - 25 miles

D - 30 miles

E - Cannot be determined by the information given.


Due north, due east and then back makes a right triangle. All sides of the right triangle need to be integers which means we are looking for pythagorean triplets. The triplet with the shortest leg as 5 is 5, 12, 13.

So total distance travelled by him must be 5+12+13 = 30 miles


Hi VeritasPrepKarishma , I answered it 12 miles because I think "THE SHORTEST LEG" is the hypotenuse from the starting point to the last destination.

How must we translate this kind of word question?



Hypotenuse is always the longest side in a RIGHT TRIANGLE

Sure, I understand that hypotenuse is the longest side of the triangle. But, we often face similar problem who assume the hypotenuse as a shortcut - so although that is the longest side, we can go from start to finish via hypotenuse rather than via its legs.



Hypotenuse is definitely a shortcut but when ITS GIVEN THAT THE PATH MAKES A RIGHT TRIANGLE then it means the hypotenuse WILL ALWAYS BE THE LONGEST SIDE

If it would not be a right triangle then surely it was hard to tell if Hypotenuse is the longest side or not

Thanks

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Re: Michael drives x miles due north at arrives at Point A. He then heads   [#permalink] 27 Aug 2017, 10:10
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