The diagonals of a quadrilateral are perpendicular to each other. If $d_{1} = 2 d_{2}$ and the area is $144 ext{ cm}^{2}$, find $d_{1}$.

Question

The diagonals of a quadrilateral are perpendicular to each other. If $d_{1} = 2 d_{2}$ and the area is $144 	ext{ cm}^{2}$, find $d_{1}$.

Aicharya · Accepted Answer

Area $= \dfrac{1}{2} d_{1} d_{2} = \dfrac{1}{2}(2 d_{2}) d_{2} = d_{2}^{2} = 144 \Rightarrow d_{2} = 12$. Hence $d_{1} = 24$ cm.

The diagonals of a quadrilateral are perpendicular to each other. If $d_{1} = 2 d_{2}$ and the area is $144…