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Question
Corresponding sides of two similar triangles are in the ratio 1 : 3. If the area of the smaller triangle in 40 cm2, find the area of the larger triangle.
Solution
Since the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.
`\text{(Area of smaller triangle)}/\text{(Area of larger triangle)}=\text{(Corresponding side of smaller triangle)}^2/\text{(Corresponding side of larger triangle)}^2`
`\text{(Area of smaller triangle)}/\text{(Area of larger triangle)}1^2/3^2`
`40/\text{(Area of larger triangle)}1/9`
Area of larger triangle `= (40xx9)/(1) = 360 cm^2`
Hence the area of the larger triangle is 360` cm^2`
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