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Question
Corresponding sides of two triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, determine the area of the larger triangle.
Solution
The ratio of the areas of two similar triangles is equal to the ratio of the square of any two corresponding sides.
`\text{(Area of triangle)}/\text{(Area of larger triangle)}=\text{(Corresponding side of smaller triangle)}^2/\text{(Corresponding side of larger triangle)}^2`
`\text{(Area of triangle)}/\text{(Area of larger triangle)}= 2^2/3^2`
`48/\text{(Area of larger triangle)}= 4/9`
Area of larger triangle =`(48xx9)/4`
Area of larger triangle = 108
Hence the area of the larger triangle is ` 108 cm^2`
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