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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