Question

In the figure below the diagonals intersect at M. If EM = 5x + 1 and HM = 4x + 9, find the value of x that would prove HGFE is a rectangle.

Answer 1

Given:

HGFE is a rectangle.

EM = 5x+1

HM = 4x+9

Diagonals intersect at M.

The objective is to find the value of x.

Since the given figure is a rectangle, the diagonals will bisect each other.

So, EM = HM.

$\begin{gathered} 5x+1=4x+9 \\ 5x-4x=9-1 \\ x=8 \end{gathered}$

Hence, the value of x is 8.