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A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq . By how much were the dimensions increased?

Respuesta :

Well to get the area of 288 the dimensions would be a couple of things but 16 ft by 18 ft seems to work, so the dimensions increase by 4 ft on each side.

12+4=16
14+4=18

18*16=288

Answer:

The increment is 4

Step-by-step explanation:

We know that the area of a rectangle is its base times its height.

Then, we can establish the following equation:

(12+x)*(14+x) = 288;

On which 'x', is the increment in the length of the rectangle's sides;

Now by developing this, we get a second degree equation:

168 + 14*x + 12*x +x^2 = 288;

Reorganizing and reducing terms, we get:

x^2 + 26*x -120 = 0.

We can use the root's equation  

(-B+-sqrt(B^2-4*A*C))/2*A

Solving this we get two answers x = 4 & x = -30.

As negative lengths have no meaning, we choose x = 4.

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