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The perimeters of two similar triangles ∆ABC and ∆PQR are 35cm and 45cm respectively, then the ratio of the areas of the two triangles is

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49:81

50:81

41:81

49:89

answer is A.

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Detailed Solution

Given that perimeters of two similar triangles

Δ ABC and Δ PQR

are 35 cm and 45 cm.
The perimeter of two similar triangles ABC and PQR class 9 maths CBSE

We know that, the ratio of perimeters of two similar triangles is equal to the ratio of their corresponding sides.
Here,

Δ ABC ~ Δ PQR

.
Then,

AB PQ = BC QR = AC PR = Perimeter of ΔABC Perimeter of ΔPQR … … (1)

Substitute given perimeter values of two similar triangles

Δ ABC and Δ PQR

in eq (1).

AB PQ = BC QR = AC PR = 3545 AB PQ = BC QR = AC PR = 79 … … (2)

Apply Area of similar triangles theorem i.e., the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
substitute the value from eq(2).

ar Δ ABC ar Δ PQR = AB PQ 2 ar Δ ABC ar Δ PQR = 792 ar Δ ABC ar Δ PQR = 4981

Hence, the ratio of the areas of the two triangles is 49: 81.
The correct option is (1).

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