In the figure above, three squares and a triangle have areas

[BTGmoderatorDC]

In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B = 81, and C = 225, then X =

(A) 150
(B) 144
(C) 80
(D) 54
(E) 36



OA D

Source: Official Guide

[Jay@ManhattanReview]

In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B = 81, and C = 225, then X =

(A) 150
(B) 144
(C) 80
(D) 54
(E) 36

OA D

Source: Official Guide

Given the area of A = 144, side of square A = 12; given the area of B = 81, side of square B = 9; and given the area of C = 225, side of square C = 15.

Thus, the three sides of X are 15, 12 and 9, respectively. Since 15^2 = 12^2 + 9^2, triangle X is a right-angled triangle, whose base and height are 12 and 9. Thus, the area of triangle X = 1/2 * 12 * 9 = 54.

The correct answer: D

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B = 81, and C = 225, then X =

(A) 150
(B) 144
(C) 80
(D) 54
(E) 36

OA D

Source: Official Guide

Based on the given areas, we see that the sides of triangle x are 12, 9, and 15, so we have a 9-12- 15 right triangle. Thus, the area of the triangle is 9 x 12 x 1/2 = 54.

Answer: D