Question

MNOP is a trapezoid with median QR. Find x.

Answer 1

D. x = 7

Explanation:

Midsegment of a trapezium = ½(sum of the lengths of the parallel bases) => Trapezoid midsegment theorem

Thus:

QR = ½(NO + MP)

QR = 14

NO = 8

MP = 2x + 6

Plug in the values into the equation

14 = ½(8 + 2x + 6)

14 × 2 = ½(8 + 2x + 6)×2

28 = 8 + 2x + 6

28 = 14 + 2x

28 - 14 = 14 + 2x - 14

14 = 2x

14/2 = 2x/2

7 = x

x = 7