Q20 of 99 Page 267

The largested square is cut-out from a right-angled triangular region with length of 3 cm, 4 cm and 5 cm respectively in such a way that the one vertex of square lies on hypotenuse of triangle. Let us write by calculating the length of side of square.

Given, sides of the right angled triangle are 3 cm, 4cm and 5 cm



Let BFDE is the largest square that can be inscribed in the right triangle ABC right angled at B


Also let BF = x cm so AF = 4-x cm


In Δ ABC and Δ AFD


∠ A= ∠ A common


∠ AFD = ∠ ABC (each 90°)


Δ ABC ∼ Δ AFD (by AA similarity)


So



⇒


⇒ 3 (4 - x) = 4x


⇒ 12 - 3x = 4x


⇒ 12 = 7x


⇒ cm


Length of square =


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