Question

In the diagram below, ABC ~ DEC. What is the value of x?

Answer 1

3

Step-by-step explanation:

Similar figures have sides that are proportional. This means that the ratio of corresponding sides is the same, no matter which two corresponding sides you compare.

Using the similarity statement, we know that AB corresponds to DE and that BC corresponds to EC. This means that the ratio of AB:DE is the same as the ratio of BC:EC, giving us the proportion

`(x)/(18-x)=(5)/(25)`

Cross-multiplying, we have

x(25) = (18-x)(5)

25x = 90-5x

Add 5x to each side:

25x+5x = 90-5x+5x

30x = 90

Divide both sides by 30:

30x/30 = 90/30

x = 3

Answer 2

25/5 = 18-x/x

25x = 5(18-x)

25x = 90-5x
30x =90
x = 90/30
x = 3