CAT 2021 Slot 2 QA Question 7: If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

Question

If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

Accepted Answer

Let the diagonals of the rhombus be $p$ and $q$, where $p$ is the longer diagonal.

$\dfrac{1}{2}pq=12$
$pq=24$

The diagonals of a rhombus bisect each other at right angles. Therefore, using the side length 5,
$\left(\dfrac{p}{2} \right)^2 + \left(\dfrac{q}{2} \right)^2 = 5^2$
$p^2+q^2=100$

$(p+q)