The perimeter of a triangle is given by:
Perimeter = sum of three sides
We are given perimeter = 112 in.
Hypotenuse = 50 in.
Let us say the other two sides are a and b.
So , we have
[tex] a+b+50 =112 [/tex]
[tex] a+b =62 [/tex]
[tex] a =62-b [/tex]...............(2)
In a right angle triangle we can apply pythagorean theorem,
a² + b² = c²
here c is hypotenuse which is 50 in.
a²+b² = 50²
a²+b² = 2500............(2)
Plugging the value of a from equation (1) in (2)
[tex] (62-b)^{2}+b^{2}=2500[/tex]
[tex] 3844-124b+(b)^{2}+b^{2}=2500[/tex]
[tex]2(b)^{2}-124b+1344=0[/tex]
Factorising ,
[tex] (b-14)(b-48)=0 [/tex]
So we have two values of b
b=14 and b=48
If b=14, a=48
If b=48, a=14
Answer: The shorter leg will be 14 inches.
