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

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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) About Me  (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 60%2B20

Answer by richwmiller(17219) About Me  (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


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 2%2Ax%5E2%2B40%2Ax-9600=0 ( notice a=2, b=40, and c=-9600)





x+=+%28-40+%2B-+sqrt%28+%2840%29%5E2-4%2A2%2A-9600+%29%29%2F%282%2A2%29 Plug in a=2, b=40, and c=-9600




x+=+%28-40+%2B-+sqrt%28+1600-4%2A2%2A-9600+%29%29%2F%282%2A2%29 Square 40 to get 1600




x+=+%28-40+%2B-+sqrt%28+1600%2B76800+%29%29%2F%282%2A2%29 Multiply -4%2A-9600%2A2 to get 76800




x+=+%28-40+%2B-+sqrt%28+78400+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-40+%2B-+280%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-40+%2B-+280%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%28-40+%2B+280%29%2F4 or x+=+%28-40+-+280%29%2F4


Lets look at the first part:


x=%28-40+%2B+280%29%2F4


x=240%2F4 Add the terms in the numerator

x=60 Divide


So one answer is

x=60




Now lets look at the second part:


x=%28-40+-+280%29%2F4


x=-320%2F4 Subtract the terms in the numerator

x=-80 Divide


So another answer is

x=-80


So our solutions are:

x=60 or x=-80


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