Q. 203.7( 7 Votes )

# 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.

Answer :

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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