Question

The figures are similar. Find x.

Answer 1

14.4 is the correct answer!

5 x ? = 9

9 ÷ 5 = 1.8

8 x 1.8 = 14.4

Please let me know if I am wrong.

Answer 2

x = 14.4

Explanation:

In similar figures, corresponding sides are proportional. This means that if you have two similar figures, then the ratio of the lengths of corresponding sides in one figure will be equal to the ratio of the lengths of corresponding sides in the other figure.

Therefore, for the two similar right triangles, the ratio of the long leg to the short leg of the larger triangle is equal to the ratio of the long leg to the short leg of the smaller triangle:

`x : 9 = 8 : 5`

Solve for x:

`(x)/(9)=(8)/(5)`

`(x)/(9)* 9=(8)/(5)* 9`

`x=(72)/(5)`

`x=14.4`

Therefore, the value of x is:

`\Large\boxed{\boxed{x=14.4}}`