The length of a rectangular deck is 5 feet longer than its width, x. The area of the deck is 310 square feet. What equation can be used to determine the width of the deck?

1 Answer
seol
Jul 9, 2017

see explanation

Explanation:

The area of a quadrilateral (which includes rectangles) is #lxxw# or length times width. The area here is stated to be 310 square feet (#ft^2#).

We're told that the length is 5 feet longer than the width, and that #x# represents the width. Thus...

#l=5+x#
#w=x#
#\thereforelxxw=(5+x)\cdot(x)=310# #ft^2#

Now you have an algebraic variable question to solve.

  • #(5+x)\cdot(x)=310#
  • Apply Distributive Property: #x(5)+x(x)=310#
  • #5x+x^2=310#, moving everything to one side gets you a quadratic:
  • #x^2+5x-310=0#

Solving by Quadratic Formula

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