Quadrilateral EFGH is a rectangle in which J is the point of intersection of the

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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.

Answer:
:
Given, EFGH is a rectangle in which diagonals are intersecting at the point J.

Quadrilateral EFGH Is A Rectangle In Which J Is The Point Of...

We know that the diagonals of a rectangle bisect each other and are equal.
Then, EG

= 2 \times J F

\Rightarrow 24 x - 8 = 2 (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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