Question

The length of a rectangular carpet is 3 feet longer than twice its width. If the area of

Answer 1

Answer:

$Perimeter = 45ft$

Step-by-step explanation:

Given

Represent the Length as L and the Width as W.

So, we have the following:

$L = 2W + 3$

$Area = 65$

Required

Determine the perimeter

The area of a rectangle is calculated as thus:

$Area = L * W$

Substititute 65 for Area

$65 = L * W$

Substitute 2W + 3 for L

$65 = (2W + 3) * W$

This gives:

$65 = 2W^2 + 3W$

Equate to 0

$2W^2 + 3W - 65 = 0$

Expand:

$2W^2 + 10W - 13W - 65 = 0$

Factorize:

$2W(W + 5) - 13(W + 5) = 0$

$(2W - 13)(W + 5) = 0$

$2W - 13 = 0\ or\ W + 5 = 0$

$2W = 13\ or\ W = -5$

$W = \frac{13}{2}$ or $W = -5$

But width can't be less than 0.

So:

$W = \frac{13}{2}$

$W = 6.5$

Recall that:

$L = 2W + 3$

$L = 2 * 6.5 + 3$

$L = 16$

The perimeter is calculated as thus:

$Perimeter = 2 * (L + W)$

$Perimeter = 2 * (16 + 6.5)$

$Perimeter = 45ft$