# Algebra 2

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Abey Numkena is an interior designer. She has been asked to locate an oriental rug for a new corporate office. As a rule, the rug should cover 1/2 of the total floor area with a uniform width surrounding the rug.

a. if the dimensions of the room are 12 feet by 16 feet, write an equation to model the situation.

b. what are the dimesions of the rug?

• Algebra 2 -

Let L be the long dimension of the rug and W be the narrow dimension.

L W = (1/2) 12 x 16 = 96
For equal borders all around,
16 - L = 12 - W
Solve those two simultaneous equations.
L - W = 4 = L - 96/L
L^2 -4L +96 = 0
(L-12)(L+8) = 0
Choose the positive root.

• Algebra 2 -

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