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The given length of two sides of a right triangle or three side lengths of a triangle are integers and together form a Pythagorean triple. Find the length of the third side and tell whether it is a leg or hypotenuse. 96 and 100

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Answer:

Therefore, the length of third side is 28 and it is a leg.

Explanation:

Given that,

The length of two sides of a right angle triangle are 96 and 100.

Three sides of a right angle triangle form Pythagorean triplet.

Now,

The square of 96 is 9216, and the square of 100 is 10000.


96^(2) =9216 and
100^(2)=10000


100^(2)-96^(2)=10000-9216=784

since, square root of 784 is 28.

According to pythagorean theorem, it states that sum of the square of base and square of perpendicular is equal to square of hypotenuse.

Here,
(base)^(2)+(perpendicular)^(2)=(hypotenuse)^(2)


(hypotenuse)^(2)-(perpendicular)^(2)=(base)^(2)


100^(2) - 96^(2) = (base)^(2)


784=(base)^(2)

∴ The length of base (leg) is
√(784)=28.

Therefore, the length of third side is 28 and it is a leg.

User MattDMo
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