Question

In the sketch below, ADEF is similar to AGHI. Find the length of side h.

Answer 1

GIVEN;

We are given two similar triangles. These are triangle DEF and triangle GHI.

Required;

To find the length of side h.

Step-by-step solution;

For any given similar triangles, the corresponding sides always have the same ratio for all three sides.

We can set up these ratios as an equation as shown below;

`(DE)/(GH)=(DF)/(GI)`

Note that the same ratio will be applicable to other corresponding sides. Now we can substitute the values given;

`\begin{gathered} (20)/(32)=(30)/(h) \\ \\ Cross\text{ }multiply; \\ \\ h=(30*32)/(20) \\ \\ h=48 \end{gathered}`

Therefore,

ANSWER:

The length of side h is 48 units