A triangle with a perimeter of 13.5 cm and an area of 7.5 cm was enlarged so that the perimeter of a new triangle like
| April 11, 2021 | education
A triangle with a perimeter of 13.5 cm and an area of 7.5 cm was enlarged so that the perimeter of a new triangle like this one became 35.1 cm. What is the area of the new triangle?
The ratio of the perimeters of similar triangles is equal to the coefficient of similarity of these triangles. Then the coefficient of similarity will be equal to:
K = P2 / P1 = 35.1 / 13.5 = 2.6.
The ratio of the areas of similar triangles is equal to the squared coefficient of similarity of these triangles.
S2 / S1 = K ^ 2.
S2 / 7.5 = 2.6 ^ 2.
S2 = 6.76 * 7.5 = 50.7 cm2.
Answer: The area of the new triangle is 50.7 cm2.
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