Question

Question 20

Area of a quadrilateral ABCD is $20c{m}^2$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is
(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

Answer 1

Area of the given quadrilateral $=\frac{1}{2}$ $\times$ (Sum of altitudes) $\times$ Corresponding diagonal
$\Rightarrow 20=\frac{1}{2}(1+1.5)\times BD$ [given]
$\Rightarrow \frac{1}{2}\times 2.5\times BD=20c{m}^2$
$\Rightarrow BD=20\times \frac{2}{2.5}=\frac{40}{2.5}=16cm$