Question

What is the length of ac?

Answer 1

Explanation:

Given triangles are similar, so we setup a proportion

(140-x)/81 = x/9

solving gives x = 14

AC = 140-x = 140-14 = 126

Answer 2

The length of AC is 126 units.

Explanation:

Given information: ED=9 units, AB=81 units, EC=x and AC=140-x.

In triangle ABC and EDC,

`\angle A=\angle E` (Given)

`\angle ACD=\angle ECD` (Given)

By AA property of similarity,

`\triangle ABC\sim \angle EDC`

Both triangles ABC and EDC are similar. The corresponding sides of two similar triangles are proportional.

`(AB)/(ED)=(AC)/(EC)`

`(81)/(9)=(140-x)/(x)`

`9=(140-x)/(x)`

`9x=140-x`

`9x+x=140`

`10x=140`

Divide both sides by 10.

`x=14`

The value of x is 14. So, the length of AC is

`AC=140-14=126`

Therefore the length of AC is 126 units.