# Find the area of a right-angled triangle if its legs and hypotenuse are 28 and 100 respectively

May 31, 2020 | Education

| AB = 100, AC = 28

By the Pythagorean theorem, we find the second leg:

AB2 = AC2 + BC2

100 ^ 2 = 28 ^ 2 + BC ^ 2

BC ^ 2 = 10000-784

BC ^ 2 = 9216

BC = √9216

If there is no table of squares at hand, then we decompose 9216 into factors:

BC = √9216 = √4 * 2304 = √4 * 4 * 576 = √4 * 4 * 4 * 144 = 2 * 2 * 2 * 12 = 96

The area of any triangle is equal to half the product of the height and the side to which the height is drawn. In a right-angled triangle, the height coincides with one of the legs, it turns out that the area of the right-angled triangle is half the product of the legs.

SABC = (AC * BC) / 2 = (28 * 96) / 2 = 1344

Answer: 1344

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