Question

The perimeters of two similar triangles are 15cm and 20cm respectively so what would be the ratio of their areas ?

Answer 1

Answer:

9 : 16

Explaination:

Ratio of perimeters of two similar triangles is equal to the ratio of the corresponding sides of the triangle ---- (1)

Also, ratio of areas of two similar triangles is equal to the ratio of the squares of corresponding sides. --- (2)

From (1) and (2),

Ratio of areas of two similar triangles = Ratio of squares of their perimeters

Let the perimeters be 15x, 20x

Hence,

ANS = [ ( 15x ) ^2 / ( 20x ) ^2 ]

= [ ( 15x / 20x ) ^2 ]

= [ ( 3 / 4 ) ^2 ]

= 9 / 16

= 9 : 16