The areas of two similar triangles are `36\ c m^2` and `100\ c m^2` . If the length of a side of the smaller triangle in 3 cm, find the length of the corresponding side of the larger triangle.

Explanation

Given, area of smaller triangle= 36`cm^(2)` and area of larger triangle= 100 `cm ^(2)`
Aalso, length of a side of the larger triangle=20 cm ltbr gtLet length of the corresponding 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))`
`rArr 100/36=((20)^(2))/x^(2)rArrx^(2)=((20)^(2)xx36)/100`
`rArr 100/36=((20)^(2))/(x^(2))rArrx^(2)=((20)^(2)xx36)/100`
`rArr x^(2)=(400xx36)/100=144`
`therefore x=sqrt(144)=12 cm`
Hence, the length of corresponding side of the smaller triangle is 12 cm.