Question

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. 16 cm
• C. 18 cm
• D. 19 cm

Answer 1

The correct option is B

16 cm

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]
$\Rightarrow \frac{1}{2}\times 2.5\times BD=20c{m}^2$
$\Rightarrow BD=20\times \frac{2}{2.5}=\frac{40}{2.5}=16cm$