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# Starting from her home, Mirinda rides her bike in a straight line due

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Math Expert
Joined: 02 Sep 2009
Posts: 50058
Starting from her home, Mirinda rides her bike in a straight line due  [#permalink]

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16 Apr 2018, 05:49
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Difficulty:

15% (low)

Question Stats:

86% (01:27) correct 14% (01:37) wrong based on 57 sessions

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Starting from her home, Mirinda rides her bike in a straight line due south for 24 kilometers, then turns and rides in a straight line due west for 7 kilometers, at which point she stops. Assuming that she can ride in any direction with no barriers, what is the distance of her shortest route back home?

A. 20 kilometers
B. 22 kilometers
C. 25 kilometers
D. 28 kilometers
E. 31 kilometers

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Joined: 16 Sep 2017
Posts: 21
Re: Starting from her home, Mirinda rides her bike in a straight line due  [#permalink]

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16 Apr 2018, 06:38
The shortest distance is the hypotenuse of the right triangle so the answer is C 25 km

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Re: Starting from her home, Mirinda rides her bike in a straight line due  [#permalink]

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17 Apr 2018, 16:19
Bunuel wrote:
Starting from her home, Mirinda rides her bike in a straight line due south for 24 kilometers, then turns and rides in a straight line due west for 7 kilometers, at which point she stops. Assuming that she can ride in any direction with no barriers, what is the distance of her shortest route back home?

A. 20 kilometers
B. 22 kilometers
C. 25 kilometers
D. 28 kilometers
E. 31 kilometers

Because she first rode due south and then due west, Miranda has ridden her bike in a way that has created two legs of a right triangle. The shortest way home will be the hypotenuse of that triangle. We can let the distance = c and, using the Pythagorean theorem, we can create the equation:

24^2 + 7^2 = c^2

576 + 49 = c^2

625 = c^2

25 = c

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Starting from her home, Mirinda rides her bike in a straight line due  [#permalink]

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17 Apr 2018, 16:57
1
Bunuel wrote:
Starting from her home, Mirinda rides her bike in a straight line due south for 24 kilometers, then turns and rides in a straight line due west for 7 kilometers, at which point she stops. Assuming that she can ride in any direction with no barriers, what is the distance of her shortest route back home?

A. 20 kilometers
B. 22 kilometers
C. 25 kilometers
D. 28 kilometers
E. 31 kilometers

Miranda has created the legs of a right triangle whose hypotenuse is her shortest route back home.

This problem takes just seconds if you catch 7-24-25; it is a Pythagorean triplet.

$$7^2 + 24^2 = 25^2$$
$$49 + 576 = 625$$

Knowing what most sources list as the top four Pythagorean triplets can save a lot of time. They are 3-4-5, 5-12-13, 7-24-25, and 8-15-17

See, e.g., Bunuel Right Triangle

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Starting from her home, Mirinda rides her bike in a straight line due &nbs [#permalink] 17 Apr 2018, 16:57
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