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`

⇒ `100/36 = (20)^2/x^2`

⇒ x² = `((20)^2 xx 36)/100`

⇒ x² = `(400 xx 36)/100` = 144

∴ x = `sqrt(144)` = 12 cm

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