Question

Areas of two similar triangles are 36 cm² and 100 cm². If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle.

Answer 1

Given, area of smaller triangle = 36 cm² and area of larger triangle = 100 cm²

Also, length of a side of the larger triangle = 20 cm

Let length of the corresponding side of the smaller triangle = x cm

By property of area of similar triangle,

`(ar("larger triangle"))/(ar("smaller triangle")) = ("Side of larger triangle")^2/("Side of smaller triangle"^2)`

⇒ `100/6 = (20)^2`

⇒ `x^2 = ((20)^2 xx 36)/100`

⇒ `x^2 = (400 xx 36)/100` = 144

∴ `x = sqrt(144)` = 12 cm

Hence, the length of corresponding side of the smaller triangle is 12 cm.