Question

a rectangular deck is to be built so that the width and the length are two consecutive even integers and the perimeter is 252 ft. Find the dimensions of the deck.

Answer 1

Perimeter = 252 = 2 Width + 2 Length

Length > Width (duh ;)

Length= Width +2 ( 2 consecutive even integer)

Linear equations:

2 length + 2 width = 252

length - width = 2 ===> length = 64 feet width = 62 feet

Answer 2

Dimensions of the rectangular deck are 64 feet × 62 feet.

Explanation:

Let the length of the rectangular deck = l ft

And the width of the rectangular deck = w ft

Since width and length of the deck are two consecutive even integers,

so, l = w + 2

Now perimeter of the rectangular deck has been given = 252 ft

Then by the formula,

Perimeter = 2 (length + width)

252 = 2(l + w)

252 = 2[w + (w + 2)]

252 = 2(2w + 2)

252 = 4(w + 1)

w + 1 =
`(252)/(4)`

w = 63 - 1

w = 62 ft

Sine l = w + 2

l = 62 + 2

l = 64 ft

Therefore dimensions of the deck are 64 feet × 62 feet.