SOLUTION: Hi, can someone please help me with this word problem? I have been trying to figure out the answer for the past 4 days! It says the following: "A rectangular yard is 20 feet longer

Question 901870: Hi, can someone please help me with this word problem? I have been trying to figure out the answer for the past 4 days! It says the following: "A rectangular yard is 20 feet longer than it is wide. Determine the dimensions of the yard if it measures 100 ft diagonally.
The equation I came up with is the following:
(20+2w)(2+2w)=100ft. W=width,
40+40w+4w+4w^2=100
40+44w+4w^2-100=0
4w^2+44w-60=0
2(w^2+22w+30)=0 this is as far as I got and that's prime. I know there is a real answer not just prime. I would really appreciate your help! Thank you for your time!
Found 2 solutions by ewatrrr, richwmiller:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
diagonally...hint for Pythagorean Theorem
w^2 + (w+20)^2 = 100^2
2w^2 + 40w - 9600 = 0
w^2 + 20s - 4800 = 0 (Tossing out the negative solution for unit measure)
(w + 80)(w-60) = 0, w = 60ft and L = 80ft

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
The diagonal is the hypotenuse and the length and width are the legs .
(20+x)^2+x^2=100^2
2x^2+40 x+400 = 10000
2x^2+40x - 9600=0

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=2, b=40, and c=-9600

Square 40 to get 1600

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 2 to get 4

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

We discard negative measurements
x = 60 y=80
The length is 80 the width is 60 and the diagonal is 100

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