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Anestetic [448]
3 years ago
8

What is the length of ac?

Mathematics
2 answers:
Lelu [443]3 years ago
8 0

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.

leonid [27]3 years ago
7 0

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

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