Question

In the diagram, XW = x + 9 and RQ = 2x – 3. Solve for x.

Question 3 options:

A)

7

B)

6

C)

4

D)

5

Answer 1

Option (D). 5

Explanation:

From the given figure,

In a ΔWXY,

XR ≅ RY and QY ≅ QW

That means QR is the mid-segment.

By the theorem of mid-segments,

`QR=(1)/(2)(XW)`

(2x - 3) =
`(1)/(2)(x+9)`

2(2x - 3) = x + 9

4x - 6 = x + 9

(4x - 6) + 6 = (x + 9) + 6

4x = x + 15

4x - x = (x + 15) - x

3x = 15

x =
`(15)/(3)`

x = 5

Therefore, Option (D) will be the answer.