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In the figure above, the perimeter of ∆MNP is how much

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by BTGmoderatorLU » Sat Apr 06, 2019 2:46 pm

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Source: GMAT Paper Tests

Image

In the figure above, the perimeter of ∆MNP is how much greater than the perimeter of the shaded region?

A. \(2+\sqrt{2}\)
B. \(6\)
C. \(8\sqrt{2}\)
D. \(6+3\sqrt{2}\)
E. \(6+8\sqrt{2}\)

The OA is D
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Source: — Problem Solving |

by Jay@ManhattanReview » Mon Apr 08, 2019 3:19 am
BTGmoderatorLU wrote:Source: GMAT Paper Tests

Image

In the figure above, the perimeter of ∆MNP is how much greater than the perimeter of the shaded region?

A. \(2+\sqrt{2}\)
B. \(6\)
C. \(8\sqrt{2}\)
D. \(6+3\sqrt{2}\)
E. \(6+8\sqrt{2}\)

The OA is D
We see ∆MNP is an isosceles rightangled triangle; thus, MN is the hypotenuse of the triangle. Length of MN = 8√2

Perimeter of ∆MNP = 8√2 + 8 + 8 = 8(2 + √2) meters

Similarly, the shaded triangle is also an isosceles rightangled triangle; thus, its hypotenuse = 5√2

Perimeter of the shaded triangle = 5√2 + 5 + 5 = 5(2 + √2) meters

The perimeter of ∆MNP is 8(2 + √2) - 5(2 + √2) = 3(2 + √2) = 6 + 3√2 greater than the perimeter of the shaded region.

The correct answer: D

Hope this helps!

-Jay
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