Question

Given the median QR and trapezoid MNOP what is the value of x? 4x-16

Answer 1

8

Explanation:

Just took it on a p e x

Answer 2

Option C:

The value of x is 8.

Solution:

Given MNOP is a trapezoid.

QR is the mid-segment of the trapezoid.

NO = 4x – 16, MP = 32, QR = x + 16

The mid-segment of a trapezoid is half the of the sum of the two parallel sides.

`$QR=(1)/(2)(NO+MP)`

`$x+16=(1)/(2)(4x-16+32)`

`$x+16=(1)/(2)(4x+16)`

Do cross multiplication.

`2(x+16)=(4x+16)`

`2x+32=4x+16`

Subtract 16 on both sides.

`2x+16=4x`

Subtract 2x on both sides of the equation.

`16=2x`

Divide by 2 on both sides of the equation.

8 = x

x = 8

Option C is the correct answer.

Hence the value of x is 8.