Question

Adjacent sides of a rectangle are of lengths $7cm$ and $24cm$. Find the length of its diagonals

Answer 1

Given :

Adjacent side are 7 cm and 24 cm for rectangle

$\therefore$ Let's say we have rectangle $ABCD$

Opposite sides of rectangle are equal in length

$\therefore AD=BC=7cm$

$AB=CD=24cm$

Now $\angle A={90}^{\circ }$ In $\Delta ABD$

$B{D}^2=A{D}^2+A{B}^2$ [By Pythagoras theorem]

$B{D}^2=(7{)}^2+(24{)}^2$

$B{D}^2=49+576$

$B{D}^2=625$

$BD=25cm$

Length of diagonals is same in rectangle

$\therefore BD=AC=25cm$

$\therefore$ length of diagonals is $25cm$.