To determine the length of the hypotenuse, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right-angled 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.
In this case, the sides are 12, 16, and 20. We can label the hypotenuse as 'c', and the other two sides as 'a' and 'b'. We want to find the length of the hypotenuse, which is 'c'.
Using the Pythagorean Theorem, we have:
c^2 = a^2 + b^2
Plugging in the values, we have:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
Taking the square root of both sides, we have:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20 units.
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The Pythagorean Theorem is a mathematical principle that helps us find the length of the hypotenuse in a right-angled triangle. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have a right-angled triangle with sides measuring 12 and 16 units. We want to find the length of the hypotenuse, which we can label as 'c'. By applying the Pythagorean Theorem, we can set up the equation c^2 = a^2 + b^2, where 'a' and 'b' represent the lengths of the other two sides.
We then substitute the given values into the equation: c^2 = 12^2 + 16^2. This simplifies to c^2 = 144 + 256, which further simplifies to c^2 = 400.
Next, we take the square root of both sides to solve for 'c'. The square root of 400 is 20, so c = 20.
Therefore, the length of the hypotenuse in this right-angled triangle is 20 units.