Question

In the given figure, DE || BC. If AD = 3 cm, AB = 7 cm and EC = 3 cm, then the length of AE is ______.

Options

• 2 cm

• 2.25 cm

• 3.5 cm

• 4 cm

Answer 1

In the given figure, DE || BC. If AD = 3 cm, AB = 7 cm and EC = 3 cm, then the length of AE is 2.25 cm.

Explanation:

Given, AD = 3 cm, AB = 7 cm, EC = 3 cm.

Let AE = x cm

∴ AC = AE + EC = x + 3 cm

As we know that

`(AD)/(AB) = (AE)/(AC)`

`\implies 3/7 = x/(x + 3)`

`\implies` 3(x + 3) = 7x

`\implies` 3x + 9 = 7x

`\implies` 7x – 3x = 9

`\implies` 4x = 9

`\implies` x = `9/4` = 2.25 cm

∴ length of AE = 2.25 cm