Question

What is AE ? Enter your answer in the box. units Two segments A D and B C intersect at point E to form two triangles A B E and D C E. Side A B is parallel to side D C. A E is labeled 2 x plus 10. E D is labeled x plus 3. A B is 10 units long. D C is 4 units long

Answer 1

Answer:

The length of AE is 20 units.

Step-by-step explanation:

Given two segments AD and BC intersect at point E to form two triangles ABE and DCE. Side AB is parallel to side DC. A E is labeled 2x+10. ED is labeled x+3. AB is 10 units long and DC is 4 units long.

we have to find the length of AE

AB||CD ⇒ ∠EAB=∠EDC and ∠EBA=∠ECD  

In ΔABE and ΔDCE

∠EAB=∠EDC      (∵Alternate angles)

∠EBA=∠ECD      (∵Alternate angles)

By AA similarity, ΔABE ≈ ΔDCE

therefore, $\frac{AE}{ED}=\frac{AB}{CD}$

⇒ $\frac{2x+10}{x+3}=\frac{10}{4}$

⇒ $8x+40=10x+30$

⇒ $x=5$

Hence, AE=2x+10=2(5)+10=20 units

The length of AE is 20 units.