# The area of an isosceles triangle is 12cm2, the perimeter is 16cm, and the height is 4cm. What is the length of the side?

January 12, 2021 | education

| The area of the rectangle is equal to half the product of the base and the height, S = 1/2 ah, where S is the area, a is the base, h is the height. We know the area and height, S = 12 cm ^ 2, h = 4 cm. Let us express from the formula a.

S = (ah) / 2;

ah = 2S;

a = 2S / h;

a = (2 * 12) / 4 = 24/4 = 6 (cm).

The perimeter of a triangle is equal to the sum of the lengths of its sides. In an isosceles triangle, the two sides are equal, they are called lateral sides. Then the formula for the perimeter of an isosceles triangle is P = a + 2b, where P is the perimeter, a is the base, b is the side. express from the formula b.

2b = P – a;

b = (P – a) / 2;

b = (16 – 6) / 2 = 10/2 = 5 (cm).

Answer. 5 cm.

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