Question

Find x

In rectangle QRST, QS = 5x - 31 and RT = 2x + 11.
Find the lengths of the diagonals of QRST.


A.4
B.6
C.14
D.16

Answer 1

C

Explanation:

The diagonals of a rectangle are congruent, then

5x - 31 = 2x + 11 ( subtract 2x from both sides )

3x - 31 = 11 ( add 31 to both sides )

3x = 42 ( divide both sides by 3 )

x = 14

Then

RT = 2x + 11 = 2(14) + 11 = 28 + 11 = 39

The diagonals are each 39 units