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Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals as shown below.

Find the value of x if JF = 8x + 4 and EG = 24x – 8.

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answer is A.

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Detailed Solution

Given, quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals.
Question Image

We know that a rectangle is a parallelogram in which the angles are at

90 ∘

.
Also, both of its diagonals are equal and bisect each other.
On the basis of this property, we can say that in the rectangle EFGH,

J F = E J = J G

Next, from the given diagram, we have,

E G = E J + J G E G = J F + J F E G = 2 J F

Substituting the values of EG and JF, as 24x – 8 and 8x + 4 respectively, we get,

24 x − 8 = 2 (8 x + 4)

Now, we will solve this equation for the value of x as follows,

24 x − 8 = 16 x + 8 24 x − 16 x = 8 + 8 8 x = 16 x = 168 x = 2

So, the value of x is obtained as 2.
Hence, the correct option is (1).

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