The perimeter of an isosceles triangle is 112 cm, and its two sides are in a ratio of 2: 3. Find the sides of the triangle.
July 28, 2021 | education|
1. A, B, C – the vertices of the triangle.
2. By the condition of the problem AB: AC = 2: 3. Therefore, AC = 3AB / 2.
3. Further calculations are performed using the formula for calculating the perimeter of a triangle:
AC + AB + BC = 112 centimeters.
BC = AB, since this triangle is isosceles.
4. Substitute AB instead of BC and 3AB / 2 instead of AC into the original formula:
3АВ / 2 + 2АВ = 112.
7AB / 2 = 112.
AB = 2 x 16 = 32 centimeters.
AC = 3 x 32: 2 = 48 centimeters.
Answer: AC = 48 centimeters, AB = BC = 32 centimeters.
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