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jmc

geometry junior

Problem

A square with area is inscribed in a square with area , with each vertex of the smaller square on a side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length , and the other of length . What is the value of ?
problem
(A)
(B)
(C)
(D)
Solution
The total area of the four congruent triangles formed by the squares is . Therefore, the area of one of these triangles is . The height of one of these triangles is and the base is . Using the formula for area of the triangle, we have . Multiply by on both sides to find that the value of is .
Final answer
C