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प्रश्न
Areas of two similar triangles are in the ratio 144 : 49. Find the ratio of their corresponding sides.
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उत्तर
Let the areas of two similar triangles be A1, A2 and their corresponding sides be S1, S2 respectively.
∴ `(A_1)/(A_2) = 144/49` ...(i) [Given]
∴ `(A_1)/(A_2) = (S_1^2)/(S_2^2)` ...[Theorem of areas of similar triangles]
∴ `144/49 = (S_1^2)/(S_2^2)` ...[From (i)]
∴ `(S_1)/(S_2) = 12/7` ...[Taking square root of both sides]
∴ The ratio of the corresponding sides of the given triangles is 12 : 7.
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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`
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Therefore,
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= `square/square`
