Question

If triangle ACD ~ triangle ABE, find the value of x.

Answer 1

Answer:

x = 16

Explanations:

Since △ACD ~ △ABE, it means that:

CD/AD = BE/AE..........(*)

CD = 3x + 8

AD = AE + ED

AD = (x - 1) + 27

AD = x + 26

BE = 20

AE = x - 1

Substituting CD, AD, BE, and AE into equation (*)

(3x+8)/(x+26) = 20/x-1

Cross multiply:

(3x+8)(x-1) = 20(x+26)

3x² - 3x + 8x - 8= 20x + 520

3x²- 15x - 528 = 0

Divide through by 3

x² - 5x - 176 = 0

Solving the quadratic equation above for the values of x

x² - 16x + 11x - 176 = 0

x(x - 16) + 11 (x - 16) = 0

(x - 16)(x + 11) = 0

If x - 16 = 0

x = 16

If x + 11 = 0

x = -11

x cannot be -11 because x = -11 will make side CD and AE to be negative, and the sides of a triangle cannot be negative.

Therefore, x = 16