# The side of an isosceles triangle is 25 and the base is 48. Find the area of this triangle.

October 14, 2021 | education

| In an isosceles triangle, the height is the median.

Therefore, AK = ½ AC = ½ * 48 = 24.

The ABK triangle is rectangular.

By the Pythagorean theorem AB ^ 2 = BK ^ 2 + AK ^ 2.

BK ^ 2 = AB ^ 2 – AK ^ 2.

BK ^ 2 = 25 ^ 2 – 24 ^ 2 = (25 – 24) (25 + 24) = 1 * 49 = 49 = 72.

BK = 7.

S = ½ AC * BK = ½ * 48 * 7 = 168.

Answer: the area of the triangle is 168.

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