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

20 units

Explanation:

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Answer 2

The length of AE is 20 units.

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,
`(AE)/(ED)=(AB)/(CD)`

⇒
`(2x+10)/(x+3)=(10)/(4)`

⇒
`8x+40=10x+30`

⇒
`x=5`

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

The length of AE is 20 units.