How do you find the leg of a right triangle
Asked by admin @ in Mathematics viewed by 277 People
What length is the shorter leg of a right triangle that has hypotenuse 50 in long and its perimeter is 112 inches?
Asked by admin @ in Mathematics viewed by 277 People
What length is the shorter leg of a right triangle that has hypotenuse 50 in long and its perimeter is 112 inches?
Answered by admin @
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
...............(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)
Factorising ,
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.
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