SOLUTION: find the lengths of each side of the right triangle short leg is 2x+1 long leg is 11x+5 hypotenuse is 12x+1 I know that first you're suppose to write the problem out like this

Question 841172: find the lengths of each side of the right triangle
short leg is 2x+1
long leg is 11x+5
hypotenuse is 12x+1
I know that first you're suppose to write the problem out like this
(12x+1)^2=(2x+1)^2+(11x+5)^2
but after this I got lost
please help and break it down as much as possible
please and thank you :D
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
So far so good. Now we just need to solve for x.

Now from here, you could factor, but I like using the quadratic formula (since it always works for any quadratic)

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=19, b=-90, and c=-25

Negate -90 to get 90

Square -90 to get 8100 (note: remember when you square -90, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 19 to get 38

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

Now because the hypotenuse is , this means that when the hypotenuse will be . But we can't have a negative length. So cannot be allowed as a solution.

That means is the only solution.

Now plug in into each expression

Short Leg:

Long Leg:

Hypotenuse:

=========================================================

Summary:

Short Leg: 11 units

Long Leg: 60 units

Hypotenuse: 61 units
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