The sides of the triangle are 5: 3: 7. Find the sides of a similar triangle, in which the difference

univerkov | August 3, 2021 | education

The sides of the triangle are 5: 3: 7. Find the sides of a similar triangle, in which the difference between the larger and smaller sides is 2 cm.

Let the length of the segment AC = 3 * X cm, the length of the segment AB = 5 * X cm, the length of the segment BC = 7 * X cm.

Since triangles ABC and A1B1C1, by condition, are similar, then A1C1 = A1C1 = 3 * Y cm, A1B1 = 5 * Y cm, B1C1 = 7 * Y cm.

By condition, B1C1 – A1C1 = 2 cm.

7 * Y – 3 * Y = 2.

Y = 2/4 = 0.5.

Then A1C1 = 3 * 0.5 = 1.5 cm, A1B1 = 5 * 0.5 = 2.5 cm, B1C1 = 7 * 0.5 = 3.5 cm.

Answer: The lengths of the sides of the triangle are 1.5 cm, 2.5 cm, 3.5 cm.

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