Question

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.

Answer 1

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 :

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

"the area of the new rectangular deck is 68 ft2 larger than the area of the original deck" 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