Find the length of the hypotenuse of an isosceles right-angled triangle with an area of 100cm².
July 30, 2021 | education|
From the condition we know that we are given a right-angled isosceles triangle and its known area is 100 cm ^ 2. We need to find the length of the hypotenuse.
We start by recalling the formula for finding the area of a right-angled triangle, through the lengths of the legs:
S = 1/2 * a * b;
The lengths of the legs are the same, since the triangle is isosceles. Let’s denote by x cm the length of the legs and write the equation:
100 = 1/2 * x ^ 2;
x ^ 2 = 200;
x = 10√2 cm legs.
Let’s apply the Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2;
c = √ (10√2) ^ 2 + (10√2) ^ 2 = √400 = 20 cm.
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