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QID : 60 - Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 2:3, and area of Δ
APQ is 8 sq cm, what is the area of trapezium PQCB?

Asked by aryap7964 6th December 2017, 4:21 PM
Answered by Expert
Answer:
begin mathsize 16px style SInce space PQ parallel to BC
angle APQ equals angle ABC
angle AQP equals angle ACB
rightwards double arrow triangle APQ tilde triangle ABC
rightwards double arrow AP squared over AB squared equals fraction numerator Area left parenthesis APQ right parenthesis over denominator Area left parenthesis ABC right parenthesis end fraction
rightwards double arrow fraction numerator 2 squared over denominator left parenthesis 2 plus 3 right parenthesis squared end fraction equals fraction numerator 8 over denominator Area left parenthesis ABC right parenthesis end fraction
rightwards double arrow 4 over 25 equals fraction numerator 8 over denominator Area left parenthesis triangle ABC right parenthesis end fraction
rightwards double arrow Area left parenthesis triangle ABC right parenthesis equals fraction numerator 25 cross times 8 over denominator 4 end fraction equals 50 space cm squared
rightwards double arrow Area left parenthesis PQCB right parenthesis equals Area left parenthesis triangle ABC right parenthesis minus Area left parenthesis triangle APQ right parenthesis equals 50 minus 8 equals 42 space cm squared end style
Answered by Expert 8th December 2017, 11:22 AM
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