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CBSE Class 10 Answered

Two triangles ABC and PQR  are such that  and . If the ratio of their perimeters is 3 : 5, Find the ratio of their areas.
Asked by Topperlearning User | 03 Oct, 2017, 01:52: PM
answered-by-expert Expert Answer

From the given information,

We see that (AA  rule)

So, begin mathsize 12px style AB over PQ equals BC over QR equals AC over PR equals straight k space left parenthesis say right parenthesis
end style

begin mathsize 12px style rightwards double arrow space fraction numerator space AB thin space plus thin space BC thin space plus thin space AC over denominator PQ thin space plus thin space QR thin space plus thin space PR end fraction equals straight k end style

So according to question ,

begin mathsize 12px style rightwards double arrow fraction numerator straight A space open parentheses increment space ABC close parentheses over denominator straight A space open parentheses increment space PQR close parentheses end fraction space equals space 3 squared over 5 squared equals 9 over 25 end style

( ratio of their areas is the same as the ratio of the squares of their corresponding sides.)

Answered by | 03 Oct, 2017, 03:52: PM
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