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DaniilM [7]
3 years ago
12

A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. The length of the deck

is to be expanded by 6 feet, and the width by 2 feet. If the area of the new rectangular deck is 68 ft2 larger than the area of the original deck, find the dimensions of the original deck.
Mathematics
1 answer:
leva [86]3 years ago
3 0
Let the width be W, then the length is 4W (since the width is 1/4 the length)

The area of the original deck is W*4W=4W^{2}

The dimensions of the new deck are :

length = 4W+6
width=W+2

so the area of the new deck is :

(4W+6)(W+2)= 4W^{2}+8W+6W+12= 4W^{2}+14W+12

"<span>the area of the new rectangular deck is 68 ft2 larger than the area of the original deck</span>" means that we write the equation:

4W^{2}+14W+12=68+4W^{2}

14W+12=68

14W=68-12=56

W= \frac{56}{14}= 4

the length is 4W=4*4=16    ft


Answer: width: 4, length: 16
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