Question

The area of a quadrilateral is 525 sq.m. The perpendiculars from
two vertices to the diagonal are 15 m and 20 m. What is the length
of this diagonal ?

Answer 1

The length of diagonal is $30\ m^{2}$.

Step-by-step explanation:

As given in question that the area of a quadrilateral is 525 $m^{2}$.

The perpendiculars from two vertices to the diagonal:

$h_{1} = 15\ m,\ h_{2} = 20\ m$

We have to find the length of diagonal (d).

We know that,

Area of quadrilateral = $\frac{1}{2}\times d(h_{1} \ +\ h_{2})$

525 = $\frac{1}{2}\times d(15\ +\ 20)$

525 x 2 = d x 35

$\frac{525\times2}{35} = d$

15 x 2 = d

∴ d = 30 $m^{2}$

Therefore, the length of diagonal is $30\ m^{2}$.