SOLUTION: Hello, I have a question for you. A rectangular garden is 10ft longer than it is wide. Its area is 6375 ft^2. What are its dimensions? Its width equals ___________ _ feet a

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello, I have a question for you. A rectangular garden is 10ft longer than it is wide. Its area is 6375 ft^2. What are its dimensions? Its width equals ___________ _ feet a      Log On


   

Question 338993: Hello, I have a question for you.
A rectangular garden is 10ft longer than it is wide. Its area is 6375 ft^2. What are its dimensions?

Its width equals _____________ feet and its length equals___________ feet.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"A rectangular garden is 10ft longer than it is wide. Its area is 6375 ft^2" means that x%28x%2B10%29=6375



x%28x%2B10%29=6375 Start with the given equation.


x%5E2%2B10x=6375 Distribute.


x%5E2%2B10x-6375=0 Subtract 6375 from both sides.


Notice that the quadratic x%5E2%2B10x-6375 is in the form of Ax%5E2%2BBx%2BC where A=1, B=10, and C=-6375


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-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%281%29%28-6375%29+%29%29%2F%282%281%29%29 Plug in A=1, B=10, and C=-6375


x+=+%28-10+%2B-+sqrt%28+100-4%281%29%28-6375%29+%29%29%2F%282%281%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100--25500+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-6375%29 to get -25500


x+=+%28-10+%2B-+sqrt%28+100%2B25500+%29%29%2F%282%281%29%29 Rewrite sqrt%28100--25500%29 as sqrt%28100%2B25500%29


x+=+%28-10+%2B-+sqrt%28+25600+%29%29%2F%282%281%29%29 Add 100 to 25500 to get 25600


x+=+%28-10+%2B-+sqrt%28+25600+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-10+%2B-+160%29%2F%282%29 Take the square root of 25600 to get 160.


x+=+%28-10+%2B+160%29%2F%282%29 or x+=+%28-10+-+160%29%2F%282%29 Break up the expression.


x+=+%28150%29%2F%282%29 or x+=++%28-170%29%2F%282%29 Combine like terms.


x+=+75 or x+=+-85 Simplify.


So the possible solutions are x+=+75 or x+=+-85

However, a negative length doesn't make sense. So ignore x+=+-85


So the only solution is x+=+75 which means that the width is 75 ft and the length is 85 ft.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website.

Jim