# Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x if JF = 8x + 4 and EG = 24x - 8.

**Solution:**

Given, EFGH is a __rectangle__.

J is the point of intersection of the diagonals.

Also, JF = 8x + 4 and EG = 24x - 8.

We have to find the value of x.

FH and EG are the __diagonals__.

Given, FH and EG intersect at J.

We know that the length of both the diagonals of the rectangle are equal.

So, FH = EG

Since the diagonals bisect each other.

EG = 2(JF)

24x - 8 = 2(8x + 4)

24x - 8 = 16x + 8

24x - 16x = 8 + 8

8x = 16

x = 16/8

Therefore, the value of x = 2.

**✦ Try This: **Quadrilateral ABCD is a rectangle in which E is the point of intersection of the diagonals. Find the value of x if EB = x - 12 and AC = 12x + 6.

**☛ Also Check: **NCERT Solutions for Class 8 Maths

**NCERT Exemplar Class 8 Maths Chapter 5 Problem 160**

## Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x if JF = 8x + 4 and EG = 24x - 8.

**Summary:**

Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. The value of x if JF = 8x + 4 and EG = 24x - 8, is 2.

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