The figure above shows a path around a

The figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

2 Explanations

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Eduardo Cuan

You can calculate the hypotenuse with the Pythagorean theorem, which is: a^2 + b^2 = c^2 (c will always be the hypotenuse)

I plugged the given values:
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
10 = c

Ted walked 10 miles and Mary walked 14 miles, 4 more miles than Ted.
Mary exceeded the distance by: 4/10 = 40%

Mar 13, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Yes, you're completely right, Eduardo! Thanks for sharing your solution :)

Mar 13, 2016 • Reply

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NIKHIL BORKER

The figure shown is a right triangle.

Mary traversed the 2 legs of the triangle while Ted traversed the hypotenuse.

It is clear from the measurements that the triangle is a 3-4-5 triangle scaled up by a factor of 2. So, the 3 sides would be 6-8-10 respectively

Ted travels 10m and Mary travels 6m+8m=14m. So Mary travels 4m/10m in excess of Ted i.e. 40% in excess

Jan 23, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Great job! Yes, as you've shown, after determining that the hypotenuse of the right triangle is 10, we can calculate the % difference by subtracting the distance Mary walks (14) from the distance Ted walks (10), dividing this difference by how far Ted walks, and multiplying by 100%: (14-10)/10x100 = 40%. Thanks for contributing to the forum :)

Jan 25, 2016 • Reply