DEFG is a rectangle, DF = 5x - 5 and EG = x + 11. Find the value of x and the length of each diagonal.

Question

a. x = 4, DF = 13, EG = 13

b. x = 4, DF = 15, EG = 18

c. x = 4, DF = 15, EG = 15

d. x = 2, DF = 13, EG = 13

Answer 1

Diagonals of a rectangle are congruent (equal), so DF = EG. Substituting the given values:

5x - 5 = x + 11

4x = 16

x = 4

DF = 5x - 5 = 5(4) - 5 = 15

EG = x + 11 = 4 + 11 = 15

(c)