Question

Parts of similar triangles.
If DEF~ JHI, find EF

Answer 1

`EF = 18`

Explanation:

Given

`\triangle DE\ F` similar to
`\triangle JHI`

Required

Find
`EF`

`\triangle DE\ F` similar to
`\triangle JHI` implies that:

The corresponding sides are:

`DE \to JH`

`DF \to JI`

`EF \to HI`

`FG \to IK`

First, solve for x using the following corresponding ratios

`EF : HI = FG : IK`

This gives:

`x + 8 : 3x - 2 = 9 : 14`

Express as fraction

`(x + 8 )/( 3x - 2) = (9 )/( 14)`

Cross multiply

`14(x + 8) = 9(3x - 2)`

Open brackets

`14x + 112 = 27x - 18`

Collect like terms

`27x - 14x = 112 + 18`

`13x = 130`

Solve for x

`x = 10`

In the diagram, we have:

`EF = x +8`

`EF = 10 +8`

`EF = 18`