SOLUTION: The length of a rectangle is four more than the width. If the area of the rectangle is 621 m2, find the width and length of the rectangle. Let w be the width. Therefore w + 4 is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The length of a rectangle is four more than the width. If the area of the rectangle is 621 m2, find the width and length of the rectangle. Let w be the width. Therefore w + 4 is       Log On


   

Question 325299: The length of a rectangle is four more than the width. If the area of the rectangle is 621 m2, find the width and length of the rectangle.
Let w be the width. Therefore w + 4 is the length.
w(w +4) = 621
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
w%28w+%2B4%29+=+621 Start with the given equation.


w%5E2%2B4w+=+621 Distribute.


w%5E2%2B4w+-+621=0 Subtract 621 from both sides.


Notice that the quadratic w%5E2%2B4w-621 is in the form of Aw%5E2%2BBw%2BC where A=1, B=4, and C=-621


Let's use the quadratic formula to solve for "w":


w+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


w+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%281%29%28-621%29+%29%29%2F%282%281%29%29 Plug in A=1, B=4, and C=-621


w+=+%28-4+%2B-+sqrt%28+16-4%281%29%28-621%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


w+=+%28-4+%2B-+sqrt%28+16--2484+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-621%29 to get -2484


w+=+%28-4+%2B-+sqrt%28+16%2B2484+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--2484%29 as sqrt%2816%2B2484%29


w+=+%28-4+%2B-+sqrt%28+2500+%29%29%2F%282%281%29%29 Add 16 to 2484 to get 2500


w+=+%28-4+%2B-+sqrt%28+2500+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


w+=+%28-4+%2B-+50%29%2F%282%29 Take the square root of 2500 to get 50.


w+=+%28-4+%2B+50%29%2F%282%29 or w+=+%28-4+-+50%29%2F%282%29 Break up the expression.


w+=+%2846%29%2F%282%29 or w+=++%28-54%29%2F%282%29 Combine like terms.


w+=+23 or w+=+-27 Simplify.


So the solutions are w+=+23 or w+=+-27

Ignore the negative solution (since a negative width doesn't make sense) to find that the width is w=23 meters.