Question

Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. If JF = $8x+4$ and EG = $24x–8$, find the value of $x$.

• A. 1.5
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B

2

Given,
JF $=8x+4$ and EG $=24x-8$
Quadrilateral is a rectangle. So,
$\angle EJF={90}^{\circ },EJ=JFandEJ=JG=\frac{24x-8}{2}$
$\Rightarrow$$\frac{24x-8}{2}=8x+4$
$\Rightarrow$$24x–8=2\times (8x+4)$
$\Rightarrow$$24x–8=16x+8$
$\Rightarrow$$24x-16x=8+8$
$\Rightarrow$$8x=16$
$\Rightarrow$$x=2$