Question

if triangle abc is congruent to pqr and 4(area of abc)=25(area of pqr) then ab:pq​

Answer 1

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ANSWER..

AB : PQ = 5:2

Step-by-step explanation:

If ar(\bigtriangleup ABC) \sim ar(\bigtriangleup PQR)ar(△ABC)∼ar(△PQR)

then

Theorem: If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

here ,

\frac{4 ar(\bigtriangleup ABC)}{25 ar(\bigtriangleup PQR)} = \frac{AB^2}{PQ^2}25ar(△PQR)4ar(△ABC)=PQ2AB2 ...(1)

i.e

\frac{ar(\bigtriangleup ABC)}{ ar(\bigtriangleup PQR)} = \frac{25}{4}ar(△PQR)ar(△ABC)=425 ..(2)

using 1 and 2

\begin{gathered}\frac{AB^2}{PQ^2} = \frac{25}{4} \\\frac{AB}{PQ} = \sqrt{ \frac{25}{4}} \\\frac{AB}{PQ} = \frac{5}{2}\end{gathered}PQ2AB2=425PQAB=425PQAB=25

Hence ,

AB :PQ = 5:2..

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