Question

Hey guys! Please answer this question very fast.

∆ABC is similar to ∆PQR. If the perimeter of ∆ABC is 60cm, it's area is 81cm² and the perimeter of ∆PQR is 80cm, then find the area of ∆PQR.

The best answer will be marked as the BRAINLIEST!!​

Answer 1

Answer:

324cm²

Step-by-step explanation:

Given: Triangle ABC is similar to PQR

Perimeter of ABC = 60 cm

Perimeter of PQR = 80cm

Now Since , ABC is similar to PQR ,therefore its corresponding sides will be in proportion.

Therefore, AB/PQ = BC/QR = CA/RP

Adding numerators and denominators ,

(AB + BC + CA) / (PQ + QR + RP)

= 60/80 [From the given perimeters]

= 3 /4

Hence each ratio will be ,

3/4 ÷3

= 3/4 × 1/3

= 1/4

Therefore,

AB/PQ = 1/4

=> AB = 1/4 PQ

Similarly,

BC = 1/4 QR

CA = 1/4 RP

Now , For the area of ABC ,

1/2 × Base × Height

= 1/2 × BC ×h

= 1/2 × QR/4 × h [Proved above]........(i)

Similarly area of PQR,

1/2 × QR ×h ..........(ii)

Now , (ii) ÷ (i) We get,

QR × 4/QR

= 4

This indicated that the area of ABC exactly divides the area of PQR by 4 times

Now ,let the area of PQR be x

Hence , x/81 = 4

=> x = 324 or,

Area of PQR is 324 cm²

KEEP SMILING ;)