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
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,
[tex]\angle A=\angle E[/tex] (Given)
[tex]\angle ACD=\angle ECD[/tex] (Given)
By AA property of similarity,
[tex]\triangle ABC\sim \angle EDC[/tex]
Both triangles ABC and EDC are similar. The corresponding sides of two similar triangles are proportional.
[tex]\frac{AB}{ED}=\frac{AC}{EC}[/tex]
[tex]\frac{81}{9}=\frac{140-x}{x}[/tex]
[tex]9=\frac{140-x}{x}[/tex]
[tex]9x=140-x[/tex]
[tex]9x+x=140[/tex]
[tex]10x=140[/tex]
Divide both sides by 10.
[tex]x=14[/tex]
The value of x is 14. So, the length of AC is
[tex]AC=140-14=126[/tex]
Therefore the length of AC is 126 units.
