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

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Solution

The correct option is B 2

Given,
JF $= 8 x + 4$ and EG $= 24 x - 8$
Quadrilateral is a rectangle. So,
$∠ E J F = 90^{\circ}, E J = J F a n d E J = J G = \frac{24 x - 8}{2}$
$\Rightarrow$ $\frac{24 x - 8}{2} = 8 x + 4$
$\Rightarrow$ $24 x - 8 = 2 \times (8 x + 4)$
$\Rightarrow$ $24 x - 8 = 16 x + 8$
$\Rightarrow$ $24 x - 16 x = 8 + 8$
$\Rightarrow$ $8 x = 16$
$\Rightarrow$ $x = 2$

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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.

The correct option is B 2 Given, JF =8x+4 and EG =24x−8 Quadrilateral is a rectangle. So, ∠EJF=90∘, EJ=JF and EJ=JG=24x−82 ⇒24x−82=8x+4 ⇒24x–8=2×(8x+4) ⇒24x–8=16x+8 ⇒24x−16x=8+8 ⇒8x=16 ⇒x=2

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