The perimeter of an isosceles triangle is 42 cm. Find the sides of this triangle if the side is 3 times the base.
| September 1, 2021 | education
In an isosceles triangle, the sides are equal.
Consider an isosceles triangle ABC, in which AB and BC are the sides, AC is the base.
It is known that the lateral side of a triangle is 3 times larger than the base, which means that you can specify:
AB = BC = 3AC.
The perimeter of a triangle (P) is equal to the sum of the lengths of all its sides:
P = AB + BC + AC.
Replacing AB and BC in this expression:
P = 3AC + 3AC + AC = 7AC.
From here we calculate the length of the base – AC:
AC = P: 7 = 42: 7 = 6 cm.
Let’s find the length of each side:
AB = BC = 3 * 6 = 18 cm.
Answer: 18 cm; 18 cm; 6 cm.
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