Question

Solve for x. The triangles in each pair are similar. Please explain!! I’m so confused

Answer 1

`x = 5`

Explanation:

Given

`\triangle JDC` similar to
`\triangle JKL`

Required

Find x

To do this, we make use of the following equivalent ratios

`JK:JL = JD:JC`

This gives

`98 : 63 = 7x + 7:27`

Express as fraction

`(98 )/( 63) =( 7x + 7)/(27)`

Multiply both sides by 27

`27 * (98 )/( 63) =( 7x + 7)/(27) * 27`

`27 * (98 )/( 63) =7x + 7`

`3* (98 )/( 7) =7x + 7`

`3* 14 =7x + 7`

`42 =7x + 7`

Collect like terms

`7x = 42 - 7`

`7x = 35`

Divide both sides by 7

`x = 5`