Question

if triangle abc is similar to triangle pqr and ab:pq = 2:3 then area of triangle abc/area of triangle pqr? ​

Answer 1

Step-by-step explanation:

if ∆ ABC ~ ∆pqr then

ab:PQ = 2:3

now let's take AB:PQ = 2x:3x

all the corresponding side's ratio will be 2x:3x..

area of ∆abc = 1/2 × breath × height

phythogras Therom ,

(2x)²= x²+h²

h²= 4x²-x²

h =√3x

area of ∆abc = 1/2 × √3x × 2x

= √3x²

same for ∆pqr ,but instead of 2x -> 3x

area of ∆pqr = 1/2 × √8x × 3x

= 3√8x²/2

then,area of triangle abc/area of triangle pqr is

√3x²/3√8x²/2 = 2√3:3√8...