Question

if triangle abc is similar to triangle PQR if ab/PQ is 4/5 find ratio of areas of this two triangles​

Answer 1

Step-by-step explanation:

16:25 is the final answer

Answer 2

Given:

ΔABC ≈ ΔPOR

AB/PQ = 4/5

To Find:

ar ΔABC / ar ΔPQR = ?

Solution:

As given,

ΔABC ≈ ΔPQR

∴ AB/PQ = BC/QR = AC/PR

ar ΔABC = 1/2 × AB × BC

ar ΔPQR =  1/2 × PQ × QR

so,

ar ΔABC / ar ΔPQR = ( 1/2 × AB × BC ) / ( 1/2 × PQ × QR )

⇒ AB/PQ × BC/QR

AB/PQ = BC/QR {as given}

⇒ ( AB/PQ)²

⇒ (4/5)²

⇒ 16/25

∴ ar ΔABC / ar ΔPQR =  16/25

Hence, the ratio of areas of these two triangles​ is equal to 16/25.