A rectangular picture has an area of 30 square inches. The length of the picture is 1 inch more than the width. What is the perimeter of the picture?

L = W + 1 (inches)

Area = A = L*W = 30 sq in., so (W)*(W+1) = 30

W^2 + W - 30 = 0 = (W-5)(W+6) = 0, so W = 5 and W = -6. Discard the negative W.

P=2W + 2L = 2(5 in) + 2(6 in) = 22 inches

Answer Link

RajarshiG RajarshiG · Answer 2 · 2022-05-24T15:37:08+02:00

The perimeter of the rectangular picture is 22 inches.

What is the area of a rectangle?

The area of a rectangle is the total area covered by that rectangle.

The area of a rectangle = length × width.

What is the perimeter of the rectangle?

The perimeter of a rectangle is the total length of it's boundary.

The perimeter of a rectangle = 2(length + width)

Given, area of the picture is 30 square inches.

Let, the length of the picture is x.

Therefore, the width of the picture is (x - 1).

Now, x(x - 1) = 30

⇒ x² - x - 30 = 0

⇒ x² - 6x + 5x -3 0 = 0

⇒ x(x - 6) + 5(x - 6) = 0

⇒ (x - 6) (x + 5) = 0

⇒ x = 6 (length can't be negative)

Therefore, length of the picture is 6 inches and the width of the picture is (6 - 1) inches = 5 inches.

Hence, the perimeter of the picture

= 2(length + width)

= 2(6 + 5) inches

= 22 inches

Learn more about the perimeter of a rectangle here: https://brainly.com/question/919810

#SPJ2