Question

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

Answer 1

$\square$ABCD be a rectangle in which adjacent sides are AB = 7 cm and BC = 24 cm and AC and BD are diagonals .

In ΔABC, $\angle$ABC = 90°. [An angle of a rectangle]
By Pythagoras's theorem, we have:
AC² = AB² + BC²
$\Rightarrow$AC² = (7)² + (24)²
$\Rightarrow$AC² = 49 + 576
$\Rightarrow$AC² = 625
On taking square roots of both sides, we get:
AC = 25 cm
We know that diagonals of a rectangle are equal.
∴ AC = BD = 25 cm