Question 651402: The lengths of the sides of a right triangle are such that the shortest side is 7 inches shorter than the middle side, while the longest side (hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides.
I know to use A sq. + b sq. = c sq.
a= x-7 sq
b= x sq
c= x+1 sq
I think I would also use sq. binomial rule as well. But I just can't get it to work.
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website! The lengths of the sides of a right triangle are such that the shortest side is 7 inches shorter than the middle side, while the longest side (hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides.
I know to use A sq. + b sq. = c sq.
a= x-7 sq
b= x sq
c= x+1 sq
I think I would also use sq. binomial rule as well. But I just can't get it to work.
Let the length of the middle side be M
Then length of shortest side = M - 7
Length of longest side (hypotenuse) = M + 1
Using pythagorean theorem formula,  , where a and b are the lengths of the legs, and c is the length of the hypotenuse, we get:
(M - 4)(M - 12) = 0
M, or middle side = 4 in. (ignore as this would make shortest side, - 3 (4 - 7), and length CANNOT be negative
M, or length of middle side =  in.
Length of shortest side = 12 - 7, or  in.
Length of longest side = 12 + 1, or  in.
This is actually one of the special right triangles, or a pythagorean triple.
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
|
|
|
