A problem by Ajay Sambhriya

Level 2

ABCD = a square
EF = 18 cm
FG =12 cm
Find the area of square ABCD


The answer is 1296.

Ajay Sambhriya by Ajay Sambhriya , 27, India

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2 solutions

Ajay Sambhriya
Oct 8, 2017

2nd solution Using construction Side = 36

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Edwin Gray
Mar 2, 2019

Triangles ABE and BEF are congruent by ASA. So AE = 18, and tan(theta) = 18/s, s = side of square. Angle DEF = 2 theta, and Cos(2 theta) = (s - 18)/30. From these 2 equations, we can eliminate theta and derive the following quadratic for s: s^2 - 30s + 216 = 0, so 2s = 30 + sqrt(900 + 864) = 30 + 42, and s = 36. Therfore the area = 36^2 = 1296.

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