# The diagonal of an isosceles trapezoid is the bisector of an acute angle, and the bases are 1: 2.

August 23, 2021 | education

| **The diagonal of an isosceles trapezoid is the bisector of an acute angle, and the bases are 1: 2. the perimeter of the trapezoid is 90. Find the larger side of the trapezoid.**

The perimeter of a trapezoid is equal to the sum of the lengths of its sides.

As already established, the lengths of the sides of the trapezoid are a, a, a and 2a.

P = a + a + a + 2a = 5a;

Therefore, the length of the smaller base of the trapezoid

a = P / 5 = 90/5 = 18.

The larger base of the trapezoid is twice the size of the smaller one:

2a = 18 * 2 = 36.

Answer: the length of the larger base of the trapezoid is 36.

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