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# On a scale drawing of a triangular piece of land, the sides of the tri

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Math Expert
Joined: 02 Sep 2009
Posts: 62637
On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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26 Apr 2019, 05:39
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35% (medium)

Question Stats:

69% (01:23) correct 31% (01:24) wrong based on 551 sessions

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On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimeters. If 1 centimeter on the drawing represents 3 meters, what is the area, in square meters, of the piece of land?

A.  90
B. 180
C. 240
D. 270
E. 540

PS54602.01

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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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26 Apr 2019, 10:07
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Top Contributor
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Bunuel wrote:
On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimeters. If 1 centimeter on the drawing represents 3 meters, what is the area, in square meters, of the piece of land?

A.  90
B. 180
C. 240
D. 270
E. 540

PS54602.01

The key here is to recognize that 5, 12 and 13 represent a Pythagorean triplet, which means the triangle in question is a RIGHT TRIANGLE

So, the drawing has sides 5 cm, 12 cm, and 13 cm . . .

. . . which means the piece of land has sides 15 m, 36 m and 39 m

Area of triangle = (base)(height)/2
Area of land = (36)(15)/2 = 270

ASIDE: Other Pythagorean triplets you should know:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

Cheers,
Brent
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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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28 Apr 2019, 02:50
Bunuel wrote:
On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimeters. If 1 centimeter on the drawing represents 3 meters, what is the area, in square meters, of the piece of land?

A.  90
B. 180
C. 240
D. 270
E. 540

PS54602.01

sides ; 5:12;13
or say 15:36: 39
area will be 1/2 * 15 * 36 ; 270
IMO D
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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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03 Jun 2019, 06:03
1
GMATPrepNow
Why does this process give incorrect result?
Area in Centimetres = (5*12)/2=30
So, area in metres= 30*3=90
Ans. A
What's wrong here?

Posted from my mobile device
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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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03 Jun 2019, 06:28
1
Top Contributor
1
msu6800 wrote:
GMATPrepNow
Why does this process give incorrect result?
Area in Centimetres = (5*12)/2=30
So, area in metres= 30*3=90
Ans. A
What's wrong here?

Posted from my mobile device

I can see that you've recognized that each side on the piece of land (in meters) is THREE TIMES the length each side on the drawing (in centimeters).
e.g., 15 is THREE TIMES 5, 39 is THREE TIMES 13, and 36 is THREE TIMES 12
So, it SEEMS that the area of the big triangle should be THREE TIMES the area of the small triangle.

However, when it comes to areas, there are TWO lengths involved.
For example, the area of 1x1 square is 1
If we take each side and TRIPLE it, we get a 3x3 square.
Is the area of this bigger square three times the area of the smaller square?
No, the area of this bigger square NINE times the area of the smaller square.

The same applies to this question.
If a triangle has a base of length b and a height of length h, then the area = bh/2
If the sides are TRIPLED, the new triangle has a base of length 3b and a height of length 3h, in which case the area = (3b)(3h)/2 = 9bh/2
So, the new area is NINE TIMES the area of the original triangle.

Does that help?

Cheers,
Brent
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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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03 Jun 2019, 06:33
msu6800 wrote:
GMATPrepNow
Why does this process give incorrect result?
Area in Centimetres = (5*12)/2=30
So, area in metres= 30*3=90
Ans. A
What's wrong here?

Posted from my mobile device

msu6800
well try to use the hint given within question it says that ∆ region is 5,12,13 so it implies its a right angled ∆
now given is another info that 1 cm = 3 cm so now simply multiply each side by 3 we get 15,36,39 so its 30: 60 : 90 angled ∆
since its a right angled hypotenuse will remain 39
so 1/2 * 15 * 36 = 270

hope this helps
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On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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03 Jun 2019, 06:42
Archit3110
I understand the solution but my question is "what is wrong in getting Area in Centimetres, and then converting centimetres in Metres? Please, check my approach to solution. Where is the wrong?
Thanks.

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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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03 Jun 2019, 06:47
1
msu6800 wrote:
Archit3110
I understand the solution but my question is "what is wrong in getting Area in Centimetres, and then converting centimetres in Metres? Please, check my approach to solution. Where is the wrong?
Thanks.

Posted from my mobile device

msu6800
well area is in m^2 so you have to multiply by 3 twice ; you shall get answer then by your approach..
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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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03 Jun 2019, 06:50
Archit3110
Thanks a lot. Got it now.

Posted from my mobile device
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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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15 Sep 2019, 15:29
Also important to note.
You can solve this as follows:

(5cm*12cm)/2 = 30cm^2
1cm =3m so 1cm^2 = 9m
30(9m)= 270m
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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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12 Oct 2019, 21:44
Hi msu6800,

While your question is to Brent, I can help you with the same. In fact I made the same mistake and ended up with 90. But the key here is that the area resulting from the below highlighted portion is in $$cm^2$$ and NOT $$cm$$, as area, which is the product of two lengths, is as we all know is in square units.

Hence, if $$1$$ $$cm$$ is $$3$$ $$mt$$ then $$1$$ $$cm^2$$ will be $$3^2$$ $$mt^2$$ or $$9$$ $$mt^2$$. Plugging this info we get - $$30$$ $$cm^2$$ $$=$$ $$30 * 9$$ $$mt^2$$ $$=$$ $$270$$ $$mt^2$$

msu6800 wrote:
GMATPrepNow
Why does this process give incorrect result?
Area in Centimetres = (5*12)/2=30
So, area in metres= 30*3=90
Ans. A
What's wrong here?

Posted from my mobile device

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Re: On a scale drawing of a triangular piece of land, the sides of the tri  [#permalink]

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07 Mar 2020, 06:23
Bunuel wrote:
On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimeters. If 1 centimeter on the drawing represents 3 meters, what is the area, in square meters, of the piece of land?

A.  90
B. 180
C. 240
D. 270
E. 540

PS54602.01

Since 1 cm represents 3 meters, the sides, in meters, of the triangular piece of land are 5 x 3 = 15, 12 x 3 = 36 and 13 x 3 = 39. Furthermore, since 5-12-13 is a right triangle, 15-36-39 is also a right triangle. Therefore, the area of the triangular piece of land is half of the product of its legs (the two shorter sides), that is,

Area = ½ bh = ½ x 36 x 15 = 18 x 15 = 270 m^2

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Re: On a scale drawing of a triangular piece of land, the sides of the tri   [#permalink] 07 Mar 2020, 06:23
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