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Question
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 in which diagonals are intersecting at the point J.
We know that, the diagonals of a rectangle bisect each other and are equal.
Then, EG = 2 × JF
⇒ 24x – 8 = 2(8x + 4)
⇒ 24x – 8 = 16x + 8
⇒ 24x – 16x = 8 + 8
⇒ 8x = 16
⇒ x = 2
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