SOLUTION: Set up the following problem using a single variable and an algebraic equation. Remember to define the unknowns. The area of Laurin's new room is 182 square feet. The length is o

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Question 1097995: Set up the following problem using a single variable and an algebraic equation. Remember to define the unknowns.
The area of Laurin's new room is 182 square feet. The length is only one foot longer than the width. Determine the dimensions of Laurin's rectangular-shaped bedroom.
Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the width, in feet.

Then the length is (x+1) feet, according to the condition.


Also, from the condition you have this equation for the area


x*(x+1) = 182  ====>

x^2 + x - 182 = 0  ====>  factor left side  ====>

(x+14)*(x-13) = 0  =====>  the roots are -14 and 13, and only positive root x= 13 makes sense.


Answer.  The width of the room is 13 ft,  the length is 13+1 = 14 ft.