Question

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

Answer 1

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.