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11 Aug 2025, 09:16
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The perimeters of similar triangles ABC and PQR
are 40 cm and x cm respectively. Find x if the areas
of triangles ABC and PQR are 50 sq.cm and
200 sq.cm respectively.
(A) 20 cm (B) 30 cm (C) 40 cm (D) 80 cm
are 40 cm and x cm respectively. Find x if the areas
of triangles ABC and PQR are 50 sq.cm and
200 sq.cm respectively.
(A) 20 cm (B) 30 cm (C) 40 cm (D) 80 cm
26 Sep 2025, 23:33
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An easy question to solve
Tr(ABC)~Tr(PQR)
And according to the properties of similar triangles
AB/PQ = BC/QR = AC/PR = Perimeter(ABC)/Perimeter(PQR)
and Ar(ABC)/Ar(PQR) = (AB/PQ)^2
We have Ar(ABC)/Ar(PQR) = 50/200 = 1/4
Therefore AB/PQ = Root(1/4) = 1/2
The Perimeter will also be in the ratio of 1:2 only
Hence, Perimeter of Tr(PQR) = 2*40 = =80 cm
Tr(ABC)~Tr(PQR)
And according to the properties of similar triangles
AB/PQ = BC/QR = AC/PR = Perimeter(ABC)/Perimeter(PQR)
and Ar(ABC)/Ar(PQR) = (AB/PQ)^2
We have Ar(ABC)/Ar(PQR) = 50/200 = 1/4
Therefore AB/PQ = Root(1/4) = 1/2
The Perimeter will also be in the ratio of 1:2 only
Hence, Perimeter of Tr(PQR) = 2*40 = =80 cm
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