Triangle ABC is equal to triangle A1B1C1. The perimeter of triangle ABC is 39cm. Side A1B1 of triangle A1B1C1

| September 23, 2021 | education

Triangle ABC is equal to triangle A1B1C1. The perimeter of triangle ABC is 39cm. Side A1B1 of triangle A1B1C1 is 1.5 times smaller than side B1C1, and A1C1 is 3 cm smaller than side A1B1. Find the large side of triangle ABC.

By the statement of the problem, it is known that triangles ABC and A1B1C1 are equal.

Therefore, the corresponding sides of these triangles are also equal. Hence it follows that the perimeters of these triangles are equal.

It is known that

B1C1 = 1.5 * A1B1,

A1B1 = A1C1 + 3.

Since the perimeter P of triangle A1B1C1 is 39 cm, we have:

P = A1B1 + B1C1 + A1C1 = 39,

A1B1 + 1.5 * A1B1 + A1B1 – 3 = 39,

3.5 * A1B1 = 42,

A1B1 = 42 / 3.5 = 12.

Then B1C1 = 1.5 * A1B1 = 1.5 * 12 = 18 and

A1C1 = A1B1 – 3 = 12 – 3 = 9.

Therefore, the longest side of triangle A1B1C1 is

B1C1 = 18. This means that the longest side of triangle ABC is also 18 cm long.

Answer: 18 cm.



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