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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
Solution
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
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