Question

Sides AB and BE of a right triangle, right-angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is ______.

Options

• `13/2`cm

• `16/3`cm

• `8/3`cm

• `4/3`cm

Answer 1

Sides AB and BE of a right triangle, right-angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is `underline(16/3 "cm")`.

Explanation:-

∆ABE is a right triangle & FDGB is a square of side x cm ∆AFD ~∆ DGE    ...(AA)

`therefore(AF)/(DG)=(FD)/(GE)`   ...(CPST)

`(16-x)/x=x/(8-x)`   ...(CPST)

128 = 24x or

`x=16/3"cm"`