sarahvarghese0
contestada

Please help. I am stuck on this algebra question:
A homeowner wants to increase the size of his deck that now measures 15 feet by 18 feet. His homeowner's association declares that no deck is to be more than 928 square feet. if the length and the width of the deck are to be increased by the same amount, find, TO THE NEAREST TENTH, the maximum number of feet by which the length of the deck may be legally increased.

a) 14 feet
b)21 feet
c)28 feet
d)32 feet

Respuesta :

wikk
Right now the deck (rectangle) is 15 feet (l) by 18 feet (w).
The area is not allowed to be more than 928 square feet.

A ≤ 928
The area of a rectangle = lw
lw ≤ 928

The variable 'x' will be the max number of feet the deck can be increased.
(x + 15)(x + 18) ≤ 928

Use FOIL to solve this.
First- (x)(x)
Outer- (x)(18)
Inner- (15)(x)
Last- (15)(18)

x² + 18x + 15x + 270 ≤ 928
x² + 33x + 270 ≤ 928

Now you can either factor or do the quadratic formula.
 x² + 33x - 658 ≤ 0
(x + 47)(x - 14) ≤ 0
x = -47 ; x = 14

-47 ≤ x ≤ 14

So the number has to be greater than/equal to -47 or less than/equal to 14.

The answer is 
A) 14 feet.

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