Corresponding sides of two triangles are in the ratio `2\ :3` . If the area of the smaller triangle is `48\ c m^2` , determine the area of the larger triangle.

Options

A. `106 cm^2`
B. `110 cm^2`
C. `108 cm^2`
D. `104 cm^2`

Answer

C

Explanation

Given, ratio of corresponding sides of two similar triangles=2 : 3 or `2/3`
Area of smaller triangle.
Ratio of area of both triangles=`("Ratio of their corresponding sides")^(2)`
i.e., `(ar("smaller triangle"))/(ar("larger triangle"))=(2/3)^(2)`
`rArr 48/(ar("larger triangle"))=4/9`
`rArr` ar(larger triangle)=`(48xx9)/4=12xx9=108 cm^(2)`