# In a right-angled isosceles triangle, the hypotenuse is 7√2 centimeters. Find the area of the triangle.

August 29, 2021 | education

| Because by the condition of the problem, the triangle is isosceles, we denote the equal sides by a cm, then by the Pythagorean theorem the equality will be true:

a ^ 2 + a ^ 2 = (7√2) ^ 2,

2a ^ 2 = 28,

a ^ 2 = 14,

a = √14.

To calculate the area of a right-angled triangle, use the relationship:

S = ½ a * b, where a and b are legs.

Because According to the condition of the problem, the legs are equal, we designated them as a cm, the area will be determined by the following formula:

S = ½ a * a.

S = ½ * √14 * √14,

S = ½ * 14,

S = 7 (cm2).

Answer: the area of the triangle is 7 cm2.

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