Question

Use similar triangles EFG and IHG to find the missing distance D.

Answer 1

If we have similar triangles, we can always use proportions to find the missing side lengths. Since triangle EFG is similar to IHG, that means side EF is similar to side IH, side FG is similar to side HG, and side GE is similar to side GI. When setting up the proportions, it is important to ensure that all similar sides correspond with each other. Here are our proportions:

6.
`(48)/(60) = (d)/(80)`



7.
`(d)/(180) = (78)/(45)`



8.
`(d)/(140.4) = (27)/(18)`



9.
`(d)/(64.8) = (211.2)/(388.8)`


To solve these proportions, we cross multiply and divide. This will give us d in each triangle.

6. d = 64

7. d = 312

8. d = 210.6

9. d = 35.2