To determine if the triangle has a right angle, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume that the lengths of the sides of triangle ABC are a, b, and c, where c is the hypotenuse. Let's also assume that squares A, B, and C have areas A1, A2, and A3 respectively.
Square A has an area of 14 units², so the length of one of its sides, which is also the length of side AB of the triangle, is √14 units.
Square B has an area of 60 units², so the length of one of its sides, which is also the length of side BC of the triangle, is √60 units.
If the triangle has a right angle, then the length of side AC, which is the hypotenuse, can be found using the Pythagorean theorem:
√(a² + b²) = c
In this case, a = √14 units and b = √60 units:
√( (√14)² + (√60)² ) = √(14 + 60) = √74 units
So the length of the hypotenuse is √74 units.
To find the area of square C, which has a side length equal to the length of the hypotenuse, we can square the length of the hypotenuse:
(√74)² = 74 units²
Therefore, the area of square C must be 74 units² for the triangle to have a right angle.
A triangle is drawn and squares are created from the lengths of each side. Square A has an area of 14 units² and Square B has an area of 60 units². What must be the area of the 3rd square for triangle to have a right angle
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