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Question
In the following figure RP : PK= 3 : 2, then find the value of A(ΔTRP) : A(ΔTPK).

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Solution
Ratio of the areas of two triangles with common or equal heights is equal to the ratio of their corresponding bases.
`(A(triangleTRP))/(A(triangleTPK))`
`="RP"/"PK"`
`=3/2`
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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`
