SOLUTION: the length of a rectangle is five feet less than twice the width. its area is 375 square feet. Find its dimensions. I need to know how to work it out.. Or just a equation

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the length of a rectangle is five feet less than twice the width. its area is 375 square feet. Find its dimensions. I need to know how to work it out.. Or just a equation      Log On


   

Question 692302: the length of a rectangle is five feet less than twice the width. its area is 375 square feet. Find its dimensions. I need to know how to work it out.. Or just a equation
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Set-Up
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A = L * W (Area of a rectangle)
Given: A = 375, L = 2W - 5
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Solution:
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Substitute the given information into the equation for the area of a rectangle
%28375%29+=+%282W+-+5%29+%2A+W Simplify
375+=+2W%5E2+-+5W Subtract 128 from both sides
0+=+2W%5E2+-+5W+-+375
Use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 2W%5E2%2B-5W%2B-375+=+0) has the following solutons:

W%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A2%2A-375=3025.

Discriminant d=3025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+3025+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+3025+%29%29%2F2%5C2+=+15
W%5B2%5D+=+%28-%28-5%29-sqrt%28+3025+%29%29%2F2%5C2+=+-12.5

Quadratic expression 2W%5E2%2B-5W%2B-375 can be factored:
2W%5E2%2B-5W%2B-375+=+2%28W-15%29%2A%28W--12.5%29
Again, the answer is: 15, -12.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-375+%29


The answers were W = 15feet or -12.5feet. but since you can not have a negative width. Just use the 15
Now we can find the length
L = 2W - 5
Plug 15 in for W
L+=+2%2A%2815%29+-%285%29
L+=+30+-+5
highlight_green%28L+=+25+feet%29