SOLUTION: Find the missing side and the hypotenuse of a right triangle that has one side equal to 293 cm and a perimeter of 1010 cm. Do not round intermediate results. Round only final an

Algebra ->  Triangles -> SOLUTION: Find the missing side and the hypotenuse of a right triangle that has one side equal to 293 cm and a perimeter of 1010 cm. Do not round intermediate results. Round only final an      Log On


   

Question 805447: Find the missing side and the hypotenuse of a right triangle that has one side equal to 293 cm and a perimeter of 1010 cm.
Do not round intermediate results. Round only final answers. Round to the nearest whole.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Side lengths h, x, y.
h is for hypotenuse.

Perimeter, h%2Bx%2By=1010.
Let one side equal y=293.
Allows for statement, h%2Bx%2B293=1010.
Simplify a bit: h%2Bx=717.

Pythagorean Theorem lets us say
x%5E2%2By%5E2=h%5E2
x%5E2%2B293%5E2=h%5E2.

System of two equation with unknowns x and h:
x%5E2%2B293%5E2=h%5E2 and h%2Bx=717

Take your pick. Use the perimeter equation for a formula for either h or x and substitute into the pythagorean equation. If doing as h=717-x, then make x%5E2%2B293%5E2=%28717-x%29%5E2
x%5E2%2B293%5E2=717%5E2-2%2A717x%2Bx%5E2
Note the x%5E2 on both sides.
293%5E2=717%5E2-2%2Ax
2x%2B293%5E2=717%5E2
2x=717%5E2-293%5E2, DIFFERENCE OF TWO SQUARES,
2x=%28717%2B293%29%28717-293%29
highlight%28x=%281%2F2%29%28717%2B293%29%28717-293%29%29
'
Just compute x and use it to compute h.
Reminder: highlight%28h=717-x%29