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Question
In ΔABC, DE || AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is ______.
Options
`("ac")/"b"`
`("ac")/("b" + "c")`
`("ab")/"c"`
`("ab")/("b" + "c")`
MCQ
Fill in the Blanks
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Solution
In ΔABC, DE || AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is `underlinebb((ac)/(b + c))`
Explanation:
DE ∥ AB, triangles DEC ∼ ABC.
`(DE)/(AB) = (CE)/(AC)`
Substitute values
DE = x
AB = a
CE = c
AC = b + c (since AE = b and EC = c)
`x/a = c/(b+c)`
`x = (ac)/(b + c)`
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