# Find the area of an isosceles triangle, the side of which refers to the base as 13:10, and the height to the base is 36 cm.

July 22, 2021 | education

| Let the side of this triangle be 13x and the base 10x. The height drawn to the base of the isosceles triangle is the median and bisects the base. Thus, the side, half of the base and the height form a right-angled triangle. According to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse:

36 ^ 2 + (5x) ^ 2 = (13x) ^ 2;

1296 + 25x ^ 2 = 169x ^ 2;

144x ^ 2 = 1296;

x ^ 2 = 1296/144 = 9;

x = √9 = 3.

Therefore, the base of this triangle is 10 * 3 = 30 cm.

The area of a triangle is equal to half the product of a side by the height drawn to it:

S = 0.5 * 30 * 36 = 540 cm2.

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