Question

Area of a right triangle is 24 cm2 and the square of

sum of the perpendicular sides is 196.

Taking the perpendicular sides as x metres and y

metres,​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Area of a right triangle is 24 square cm}$

$\textsf{and the square ofsum of the perpendicular sides is 196}$

$\underline{\textsf{To find:}}$

$\textsf{The perpendicular sides}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the perpendicular sides of the}$

$\textsf{given right triangle be x and y}$

$\textsf{Area of the triangle=24 square cm}$

$\implies\mathsf{\dfrac{1}{2}{\times}x{\times}y=24}$

$\implies\mathsf{xy=48}$

$\implies\mathsf{y=\dfrac{48}{x}}$....(1)

$\textsf{Also}$

$\mathsf{(x+y)^2=196}$

$\implies\mathsf{x+y=14}$....(2)

$\textsf{Using (1) in (2)}$

$\mathsf{x+\dfrac{48}{x}=14}$

$\mathsf{\dfrac{x^2+48}{x}=14}$

$\mathsf{x^2-14x+48=0}$

$\mathsf{(x-6)(x-8)=0}$

$\implies\mathsf{x=6,8}$

$\textsf{when x=6, y=8}$

$\textsf{when x=8, y=6}$

$\underline{\textsf{Answer:}}$

$\textsf{The perpendicular sides are 6cm, 8cm}$