Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and

Question

nekit [7.7K]

2 years ago

9

Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and

DF = x - 2 . What is the value of x?

Mathematics

1 answer:

Norma-Jean [14] · Answer 1 · 2022-08-14T02:34:27+03:00

X=8.

Following the similarity statement, we know that AC is to DF as BC is to EF. The ratio would be:

24/(x-2) = 20/5

Cross multiply:
24*5 = 20(x-2)

Use the distributive property:
120 = 20x - 40

Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x

Divide both sides by 20:
160/20 = 20x/20
8 = x