Question

DEFG is a rectangle. DF = 5x - 3and EG = x + 5. Find the value of x and the length of each diagonal.

a. x = 1, DF = 6, EG = 6
b. x = 2, DF = 7, EG = 12
c. x = 2, DF = 6, EG = 6
d. x = 2, DF = 7, EG = 7

Answer 1

Answer: d. x = 2, DF = 7, EG = 7
Solution:
by ratio: DF : EG
5x - 3 = x + 5
Solving for x:
5x -x = 5 + 3
x = 2
Substituting x=2 in the expression
DF = 5x -3 = 5(2) - 3 = 7
EG = x + 5 = 2 + 5 = 7

Answer 2

d. x = 2, DF = 7, EG = 7

DF is equivalent to EG; Therefore, the equation would be like this:

5x - 3 = x + 5
Transfer 3 and x to their opposite side and change their signs.

5x - x = 5 + 3
4x = 8
Find x. Divide both sides by 4.

4x / 4 = 8 / 4
x = 2

Subsitute x in the equation to find the length of each diagonal.

DF = 5x - 3 = 5(2) - 3 = 10 - 3 = 7 ; DF = 7
EG = x + 5 = 2 + 5 = 7 ; EG = 7