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Question
In the figure, PQ ⊥ BC, AD ⊥ BC. To find the ratio of A(ΔPQB) and A(ΔPBC), complete the following activity.
Given: PQ ⊥ BC, AD ⊥ BC
Now, A(ΔPQB) = `1/2 xx square xx square`
A(ΔPBC) = `1/2 xx square xx square`
Therefore,
`(A(ΔPQB))/(A(ΔPBC)) = (1/2 xx square xx square)/(1/2 xx square xx square)`
= `square/square`
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Solution
Given: PQ ⊥ BC, AD ⊥ BC
Now, A(ΔPQB) = `1/2` × BQ × PQ
A(ΔPBC) = `1/2` × BC × PQ
Therefore,
`(A(ΔPQB))/(A(ΔPBC)) = (1/2 xx bb(BQ) xx bb(PQ))/(1/2 xx bb(BC) xx bb(PQ))`
= `bb(BQ)/bb(BC)`
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