# Find the area of a right-angled triangle if its hypotenuse is √52, and one of the legs is 6.

March 24, 2021 | education

| According to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

Let the second leg be x cm.

Let’s use the formula, compose and solve the equation:

x ^ 2 + 6 ^ 2 = (√52) ^ 2,

x ^ 2 + 36 = 52,

x ^ 2 = 16,

x = 4 cm.

The area of a right-angled triangle is half the product of its legs:

1/2 * 4 * 6 = 12 cm2.

Answer: the area of a right-angled triangle is 12 cm2.

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