Question

What is the length of ac?

Answer 1

Answer:

The length of AC is 126 units.

Step-by-step 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.

$\frac{AB}{ED}=\frac{AC}{EC}$

$\frac{81}{9}=\frac{140-x}{x}$

$9=\frac{140-x}{x}$

$9x=140-x$

$9x+x=140$

$10x=140$

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.

Answer 2

Answer:

Step-by-step 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