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

Anabella Gilbert

Anabella Gilbert

Answered question

2023-01-21

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

Answer & Explanation

Bellitifya

Bellitifya

Beginner2023-01-22Added 6 answers

The area's dimensions are enlarged by x.
Thus, the new dimensions of the rectangle are 12+x and 14+x.
Thus, since the area is 288,
(12+x)(14+x)=288
Spread out the binomials.
x2+26x+168=288
x2+26x120=0
(x+30)(x4)=0
x=30ssssorssssx=4
Since the box's dimensions were increased, the answer will be positive: x=4.
We can check. The new dimensions would be 16 and 18, and 16×18=288.

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