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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