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Q.

Two triangles ABC and PQR are similar, if BC : CA : AB = 1 : 2 : 3, then  QRPR  is _______.


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a

13

b

12

c

12

d

23 

answer is B.

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Detailed Solution

Triangles are said to be similar if they have the same shape, but same sizes may not be necessary.
Here the given two triangles ABC and PQR are similar.
ΔABC ∼ ΔPQR
Properties of similar triangles are like corresponding angles will be the same and corresponding sides will be in the same proportions.
∠A = ∠P, ∠B = ∠Q, ∠C = ∠R and  ABPQ = BCQR = ACPR .
1454(1).jfif1454(2).jfifHere for triangle ABC, it is given that BC : CA : AB = 1 : 2 : 3
It is represented in ratio form as  BC1 = CA2 = AB3. Assuming constant one side BC = k, so the equation becomes  k1 = CA2 = AB3.
k1 = CA2. So, CA = 2k.
And k1 = AB3. So, AB = 3k
As Triangle ABC and PQR are similar triangle,
ABPQ = BCQR = ACPR   So, BCQR = ACPR
Putting value BC = k and CA = 2k in above equation,
kQR = 2kPR
Simplifying, k2k = QRPR,
So, 12 = QRPR.
So, QRPR = 12 So, Option (2) is the correct answer.
 
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