SOLUTION: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and flower bed is 165mē. What is the width of the flower bed?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and flower bed is 165mē. What is the width of the flower bed?       Log On


   

Question 325298: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and flower bed is 165mē. What is the width of the flower bed?
Let x be the width of the flowerbed
(8+2x)(4+2x)=165
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%288%2B2x%29%284%2B2x%29=165 Start with the given equation.


32%2B16x%2B8x%2B4x%5E2=165 FOIL


32%2B16x%2B8x%2B4x%5E2-165=0 Subtract 165 from both sides.


4x%5E2%2B24x-133=0 Combine like terms.


Notice that the quadratic 4x%5E2%2B24x-133 is in the form of Ax%5E2%2BBx%2BC where A=4, B=24, and C=-133


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-%2824%29+%2B-+sqrt%28+%2824%29%5E2-4%284%29%28-133%29+%29%29%2F%282%284%29%29 Plug in A=4, B=24, and C=-133


x+=+%28-24+%2B-+sqrt%28+576-4%284%29%28-133%29+%29%29%2F%282%284%29%29 Square 24 to get 576.


x+=+%28-24+%2B-+sqrt%28+576--2128+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-133%29 to get -2128


x+=+%28-24+%2B-+sqrt%28+576%2B2128+%29%29%2F%282%284%29%29 Rewrite sqrt%28576--2128%29 as sqrt%28576%2B2128%29


x+=+%28-24+%2B-+sqrt%28+2704+%29%29%2F%282%284%29%29 Add 576 to 2128 to get 2704


x+=+%28-24+%2B-+sqrt%28+2704+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-24+%2B-+52%29%2F%288%29 Take the square root of 2704 to get 52.


x+=+%28-24+%2B+52%29%2F%288%29 or x+=+%28-24+-+52%29%2F%288%29 Break up the expression.


x+=+%2828%29%2F%288%29 or x+=++%28-76%29%2F%288%29 Combine like terms.


x+=+7%2F2 or x+=+-19%2F2 Simplify.


So the solutions are x+=+7%2F2 or x+=+-19%2F2


However, 'x' is a length. So we'll ignore the negative answer.


So the width of the flower bed is x=7%2F2 which is 3.5 meters.