Question

In the parallelogram $ABCD$ shown in the figure, find the value of x. $\left[2\text{Marks}\right]$

Answer 1

We know that the diagonals of a parallelogram bisect each other.

This means that the point O bisects diagonal AC into two equivalent segments.

Thus, we know that CO and OA are congruent. $\left[1\text{Mark}\right]$

Given OC = $4x^2+5$ and OA = 41

Since, CO = OA ,
$\Rightarrow$ 4$x^2$ + 5 = 41
$\Rightarrow$ $x^2$ = 9
$\therefore$ x = 3 $\left[1\text{Mark}\right]$