Answer:
Therefore, the length of third side is 28 and it is a leg.
Step-by-step 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.
∵ [tex]96^{2} =9216[/tex] and [tex]100^{2}=10000[/tex]
⇒[tex]100^{2}-96^{2}=10000-9216=784[/tex]
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, [tex](base)^{2}+(perpendicular)^{2}=(hypotenuse)^{2}[/tex]
⇒ [tex](hypotenuse)^{2}-(perpendicular)^{2}=(base)^{2}[/tex]
⇒ [tex]100^{2} - 96^{2} = (base)^{2}[/tex]
⇒ [tex]784=(base)^{2}[/tex]
∴ The length of base (leg) is [tex]\sqrt{784}=28[/tex].
Therefore, the length of third side is 28 and it is a leg.
