Two similar triangles are given – ABC ~ A1B1C1 and A1B1C1 isosceles with base A1B1 = 8cm and perimeter 28 cm.

univerkov | February 10, 2021 | education

Two similar triangles are given – ABC ~ A1B1C1 and A1B1C1 isosceles with base A1B1 = 8cm and perimeter 28 cm. Find the sides of triangle ABC if AB = 24cm.

Since triangle A1B1C1 is isosceles, its perimeter is P = A1B1 + 2 * A1C1.

28 = 8 + 2 * A1C1.

A1C1 = (28 – 8) / 2 = 10 cm.

Let’s determine the coefficient of similarity of triangles.

K = AB / A1B1 = 24/4 = 3.

Since A1B1C1 is isosceles, then ABC is also an isosceles triangle, since they are similar in condition.

Then the sides of the triangle ABC will be equal: AC = BC = 3 * 10 = 30 cm

Answer: AB = 24, AC = BC = 30 cm.

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