Question

Prove that the ratio of the areas of two aimilar triangles is equal to the ratio of their corresponding sides

Answer 1

Answer:

Step-by-step explanation:

Sides of triangle A are a , b , c

Let say k is ratio

so sides of new triangles are  ak , bk  , ck

Area of 1st triangle = √(s(s-a)(s-b)(s-c))

s = (a+b+c)/2

S2 = (ak +  bk + ck)/2 = k(a+b+c)/2 = ks

Area of 2nd Triangle = √(ks(ks-ak)(ks-bk)(ks-ck))

= √(ksk(s-a)k(s-b)k(s-c))

=√(k^4)(s(s-a)(s-b)(s-c))

= k^2 √(s(s-a)(s-b)(s-c))

= k^2 (area of 1st Triangle)

k was ratio of side  

and k^2 is ration of Area

QED