Question

In a right-angled, triangle the area of the square drawn on the Hypotenuse is $289{cm}^2$ and the area of the square drawn on the Base is $225{cm}^2$. What will be the area of the square drawn on the Height of the triangle in ${cm}^2$?

Answer 1

Area of Square $=sid{e}^2$

Area of Square drawn on Hypotenuse $=289c{m}^2$

$Sid{e}_H=$Hypotenuse of $△=\sqrt{289}=17cm$

Area of Square drawn on Base $=225c{m}^2$

$Sid{e}_B=$Base of $△=\sqrt{225}=15cm$

We know that in a right angled triangle, by Pythagoras theorem,

$Hypotenus{e}^2=bas{e}^2+heigh{t}^2$

${17}^2={15}^2+heigh{t}^2$

$heigh{t}^2=64=8^2$

$height=8cm$

Area of Square drawn on Height $=heigh{t}^2=64c{m}^2$