SOLUTION: The legs of a right triangle differ by 2 cm. and the hypotenuse is 4 cm. more than the shorter leg. Find the sides of the triangle? please give the answer QUICKLY because I need

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The legs of a right triangle differ by 2 cm. and the hypotenuse is 4 cm. more than the shorter leg. Find the sides of the triangle? please give the answer QUICKLY because I need      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 164854: The legs of a right triangle differ by 2 cm. and the hypotenuse is 4 cm. more than the shorter leg. Find the sides of the triangle?
please give the answer QUICKLY because I need to submit this tomorrow...tnx
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
To understand this problem first draw a representation of a right triangle. Label one leg x and the other leg x-2.
Given: the hypotenuse is 4 cm. more than the shorter leg so:
label the hypotenuse x-2+4 or x+2
Now use the Pythagorean Theorem to find the value of x
%28x%29%5E2%2B%28x-2%29%5E2=%28x%2B2%29%5E2
or
x%5E2%2B%28x-2%29%28x-2%29=%28x%2B2%29%28x%2B2%29
Order of operations says we have to multiply where possible so use the FOIL method.
x%5E2%2Bx%5E2-2x-2x%2B4=x%5E2%2B2x%2B2x%2B4
combine like terms:
2x%5E2-4x%2B4=x%5E2%2B4x%2B4
Move everything to the same side.
Subtract x^2 from both sides and you get:
x%5E2-4x%2B4=4x%2B4
Subtract 4x from both sides and you get:
x^2-8x+4=4
Subtract 4 from both sides and you get:
x^2-8x=0
Factor out an x and you get:
x(x-8)=0
This statement is true when x=0 or (x-8)=0
x-8=0
add 8 to both sides and you get
x=8
x=0;x=8 However, because we are dealing with a length of a triangle x cannot=0
Therefore x=8 is the only answer to this problem.
Check your work!
your sides are 8;8-2;8-2+4 or 8;6;10
we know that 8%5E2%2B6%5E2=10%5E2
or
64+46=100
or
100=100 and therefore the answer checks out to be true.
Remember that you must always try to find a unit label for every answer. In this case it is centimeters so your final answer is 6 cm; 8 cm; and 10 cm
.
.
Paypal donations accepted through justin.sheppard.tech@hotmail.com