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A triangle with sides AB = 3, BC = 4, and AC = 5 has an inscribed square PQRS............What is the area of the square?

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A triangle with sides AB = 3, BC = 4, and AC = 5 has an inscribed square PQRS with side QR along the side AC.
What is the area of the square?

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posted Oct 13, 2020 by Anamika

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1 Answer

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Let segment AQ = X, QR = L, RC = Y, QP = L, RS = L
We can write the three equations system:
X + L + Y = 5
L / X = Tan (Angle A) = 4 /3
L / Y = Tan (angle C) = 3/4
Solving the system, L = 1,62
Area = 1,62 x 1,62 = 2,63

answer Oct 19, 2020 by anonymous

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