## LMN ~ PQR, 9 ×A(PQR ) = 16 ×A(LMN). If QR = 20 then find MN.

Given 9 ×A(PQR ) = 16 ×A(LMN)A(PQR )/ A(LMN) = 16/9…………(i)LMN ~ PQRA(PQR )/ A(LMN) = QR2/MN2 …..(ii)From (i) and (ii)QR2/MN2 = 16/9Given QR = 20202/MN2 = 16/9Taking square root on both sides20/MN = 4/3MN = 20×3/4MN = 15Hence the measure of MN is 15 units.

## If ABC ~ PQR, A( ABC) = 80, A( PQR) = 125, then fill in the blanks.

Given A( ABC) = 80, A( PQR) = 125( ABC) / A( PQR) = 80/125 = 16/25( ABC) / A( PQR) = AB2/PQ2 [Theorem of areas of similar triangles]AB2/PQ2 = 16/25Taking square root on both sidesAB/PQ = 4/5Hence AB/PQ = 4/5

## If ABC ~ PQR and AB: PQ = 2:3, then fill in the blanks.

A(ABC)/ A(PQR) = AB2/PQ2 = 22/32 = 4/9 [Theorem of areas of similar triangles]

## The ratio of corresponding sides of similar triangles is 3:5; then find the ratio of their areas

When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides.Given , the ratio of corresponding sides of the triangle is 3:5.Ratio of their areas = 32/52 [Theorem of areas of similar triangles]= 9/25Hence ratio of their areas = 9:25