Question

A field in the form of a parallelogram has an area of $432m^2.$ Find the length of its diagonal on which the perpendiculars drawn from two vertices on either side of it are $12m$ long.

Answer 1

Area of the triangle $=\frac{1}{2}\times b\times h$

$\begin{array}{c}=\frac{1}{2}\times x\times h_1+\frac{1}{2}\times x\times h_2=432\\ =\frac{1}{2}\times x\times 12+\frac{1}{2}\times x\times 12=432\\ 12x=432\\ x=36\end{array}$

Hence, the length of diagonal is $36$ m.