Question

The polygons above are similar. Write a similarity statement and solve for x. The images are not drawn to scale.

Answer 1

The correct answer is D) ABCD ~ NMLK, and x=7.

Based on the way the polygons are marked, A corresponds with N, B corresponds with M, C corresponds with L and D corresponds with K. Using this, we set up a proportion:

12/8 = (5x+1)/(5x-11)

Cross multiplying, we have:
12(5x-11) = 8(5x+1)

Using the distributive property, 
12*5x - 12*11 = 8*5x + 8*1
60x - 132 = 40x + 8

Subtract 40x from both sides:
60x - 132 - 40x = 40x + 8 - 40x
20x - 132 = 8

Add 132 to both sides:
20x - 132 + 132 = 8+132
20x = 140

Divide both sides by 20:
20x/20 = 140/20
x = 7