SOLUTION: The length of a rectangle is five less than twice the width. The area is 42 square yards. Find the dimensions of the rectangle

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Question 146769:
The length of a rectangle is five less than twice the width. The area is 42 square yards. Find the dimensions of the rectangle
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=width and y=length


Since "The length of a rectangle is five less than twice the width", this means that y=2x-5. Also, because "The area is 42 square yards", this tells us that the area equation is A=x%2Ay which becomes 42=x%2Ay


42=x%2Ay Start with the second equation


42=x%2A%282x-5%29 Plug in y=2x-5


42=2x%5E2-5x Distribute


42-2x%5E2%2B5x=0 Get all terms to the left side.


-2x%5E2%2B5x%2B42=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-2, b=5, and c=42


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%285%29+%2B-+sqrt%28+%285%29%5E2-4%28-2%29%2842%29+%29%29%2F%282%28-2%29%29 Plug in a=-2, b=5, and c=42


x+=+%28-5+%2B-+sqrt%28+25-4%28-2%29%2842%29+%29%29%2F%282%28-2%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25--336+%29%29%2F%282%28-2%29%29 Multiply 4%28-2%29%2842%29 to get -336


x+=+%28-5+%2B-+sqrt%28+25%2B336+%29%29%2F%282%28-2%29%29 Rewrite sqrt%2825--336%29 as sqrt%2825%2B336%29


x+=+%28-5+%2B-+sqrt%28+361+%29%29%2F%282%28-2%29%29 Add 25 to 336 to get 361


x+=+%28-5+%2B-+sqrt%28+361+%29%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x+=+%28-5+%2B-+19%29%2F%28-4%29 Take the square root of 361 to get 19.


x+=+%28-5+%2B+19%29%2F%28-4%29 or x+=+%28-5+-+19%29%2F%28-4%29 Break up the expression.


x+=+%2814%29%2F%28-4%29 or x+=++%28-24%29%2F%28-4%29 Combine like terms.


x+=+-7%2F2 or x+=+6 Simplify.


So the widths are x+=+-7%2F2 or x+=+6



However, since a negative width is not possible, this means that the only answer for the width is x+=+6

y=2x-5 Go back to the first equation


y=2%286%29-5 Plug in x+=+6


y=7 Simplify


So the width is 6 yards and the length is 7 lards