The sides of a triangle are in the ratio 4: 5: 7. Find the sides of a similar triangle if its perimeter is 96 cm.
April 12, 2021 | education
| Let’s denote the coefficient of similarity through x, then the sides of such a triangle will be respectively equal to 4x cm, 5x cm and 7x cm.Since the perimeter of such a triangle is 96 cm, we will compose and solve the equation:
4x + 5x + 7x = 96;
16x = 96;
x = 96: 16;
x = 6.
The coefficient of similarity is 6, then the sides of a similar triangle will be equal:
4 * 6 = 24 (cm);
5 * 6 = 30 (cm);
7 * 6 = 42 (cm).
Answer: the sides of such a triangle are 24 cm, 30 cm and 42 cm.
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