The perimeter of a rectangular carpet is 54ft. The lenght is 3ft greater than the width. How do you find the length and width?

Question

Julia Adams · Accepted Answer

Length is 15 feet; Width is 12 feet

Define: #color(white)("XX")P = " perimeter"# #color(white)("XX")L = " length"# #color(white)("XX")W = " width"# #P =2(L+W)= 54# #color(white)("XX")rarr L+W = 27# #L = W+3# #color(white)("XX")rarr (W+3)+W = 27# #color(white)("XX")rarr 2W=24# #color(white)("XX")rarr W=12# and since #L=W+3# #color(white)("XX")L=15#

Genesis Allen · Answer

undefined Let's denote the width of the rectangular carpet as $ w $ (in feet). Since the length is 3 feet greater than the width, we can express the length as $ w + 3 $.

The perimeter of a rectangle is given by the formula: $ P = 2(w + l) $, where $ P $ is the perimeter, $ w $ is the width, and $ l $ is the length.

Given that the perimeter is 54 feet, we can write the equation:

$$ 54 = 2(w + w + 3) $$

Solving for $ w $:

$$ 54 = 2(2w + 3) $$
$$ 54 = 4w + 6 $$
$$ 4w = 54 - 6 $$
$$ 4w = 48 $$
$$ w = \frac{48}{4} $$
$$ w = 12 $$

So, the width of the rectangular carpet is 12 feet.

Now, to find the length, we can use the expression for the length:

$$ l = w + 3 $$
$$ l = 12 + 3 $$
$$ l = 15 $$

Therefore, the length of the rectangular carpet is 15 feet.