Let's denote the width of the rectangle as w (in cm), and the length as l (in cm).

From the problem, we know that:

1) l = 3w - 2 (since the length is 2 cm less than thrice its width)

2) (w + 5)(l - 6) = wl + 23 (since if the width is increased by 5 cm and the length decreased by 6 cm, the area is increased by 23 cm²)

Substitute l from equation 1) into equation 2):

(w + 5)((3w - 2) - 6) = w(3w - 2) + 23
(w + 5)(3w - 8) = 3w^2 - 2w + 23
3w^2 + 15w - 40 = 3w^2 - 2w + 23
17w = 63
w = 63 / 17 = 3.71 cm (approximately)

Substitute w into equation 1) to find l:
l = 3*3.71 - 2 = 9.13 cm (approximately)

The perimeter of the rectangle is 2*(l + w) = 2*(9.13 + 3.71) = 25.68 cm (approximately)

So, the closest answer is A. 26 cm.

Question

Let's denote the width of the rectangle as w (in cm), and the length as l (in cm).

From the problem, we know that:

1) l = 3w - 2 (since the length is 2 cm less than thrice its width)

2) (w + 5)(l - 6) = wl + 23 (since if the width is increased by 5 cm and the length decreased by 6 cm, the area is increased by 23 cm²)

Substitute l from equation 1) into equation 2):

(w + 5)((3w - 2) - 6) = w(3w - 2) + 23
(w + 5)(3w - 8) = 3w^2 - 2w + 23
3w^2 + 15w - 40 = 3w^2 - 2w + 23
17w = 63
w = 63 / 17 = 3.71 cm (approximately)

Substitute w into equation 1) to find l:
l = 3*3.71 - 2 = 9.13 cm (approximately)

The perimeter of the rectangle is 2*(l + w) = 2*(9.13 + 3.71) = 25.68 cm (approximately)

So, the closest answer is A. 26 cm.

Knowee AI · Accepted Answer

Let's denote the width of the rectangle as w (in cm), and the length as l (in cm).

From the problem, we know that:

1) l = 3w - 2 (since the length is 2 cm less than thrice its width)

2) (w + 5)(l - 6) = wl + 23 (since if the width is increased by 5 cm and the length decreased by 6 cm, the area is increased by 23 cm²)

Substitute l from equation 1) into equation 2):

(w + 5)((3w - 2) - 6) = w(3w - 2) + 23
(w + 5)(3w - 8) = 3w^2 - 2w + 23
3w^2 + 15w - 40 = 3w^2 - 2w + 23
17w = 63
w = 63 / 17 = 3.71 cm (approximately)

Substitute w into equation 1) to find l:
l = 3*3.71 - 2 = 9.13 cm (approximately)

The perimeter of the rectangle is 2*(l + w) = 2*(9.13 + 3.71) = 25.68 cm (approximately)

So, the closest answer is A. 26 cm.

The length of a rectangle is 2 cm less than thrice its width. If the width is increased by 5 cm and the length decreased by 6 cm, the area is increased by 23 cm². What is the perimeter of the original rectangle?1 pointA. 26 cmB. 52 cmC. 78 cmD. 104 cm

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