Question

Can somebody please help me with this?​

Answer 1

x = 3

Solution:

Given UVWX is a parallelogram.

UV, VW, XW, UX are sides of a parallelogram.

UW and XV are diagonals of a parallelogram.

VX = 14 and BX = x + 4

Property of parallelogram:

Diagonals of a parallelogram bisect each other.

⇒ VB = BX

⇒ VX = VB + BX

⇒ VX = BX + BX (since VB = BX)

⇒ VX = 2 BX

⇒ 14 = 2(x + 4)

⇒ 14 = 2x + 8

Subtract 8 from both sides of the equation, we get

⇒ 14 – 8 = 2x + 8 – 8

⇒ 6 = 2x

Divide by 2 on both sides of the equation, we get

⇒ 3 = x

⇒ x = 3

Hence the value of x is 3.