Question

The value of x = ?

Answer key comes with:
5

2.5

6.25

4.75

Answer 1

(c) 6.25

Explanation:

You want the value of x = FG, given similar triangles DFG and RPQ.

Proportion

Corresponding sides of similar polygons are proportional. This means ...

FG/PQ = DF/RP

x/5 = 10/8

x = 5(10/8) = 50/8 . . . . multiply by 5

x = 6.25

__

Additional comment

It can be a bit confusing that x is the middle-length value. That is ...

4 : 5 : 8 = 5 : x : 10

The numbers in the second ratio of shortest-to-longest sides are 5/4 = 1.25 times those in the first ratio. Then x=1.25·5 = 6.25.