Question

Area of quadrilateral ABCD is 20 ${cm}^2$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is _______.

Answer 1

Area of quadrilateral = $20$ $c{m}^2$

Let length of $BD$ (diagonal) be $x$ $cm$.

Then,

$Area(quad.ABCD)=area△\left(ABD\right)+area△\left(ACD\right)$

Area of quad ABCD = $\frac{1}{2}\times \left(BD\right)\times \left(AL\right)+\frac{1}{2}\times \left(BD\right)\times \left(CM\right)$

$20=(\frac{1}{2}\times x\times 1)+(\frac{1}{2}\times x\times 1.5)$

$2.5x=40$

$x=\frac{400}{25}$

$x=16$ $cm$