Question

The length of a rectangle is 1 more than three times the width. If the length is diminished by 3 inches and the width is doubled, a new rectangle is formed whose perimeter is 46 inches. Find the dimensions of the original rectangle.

Answer 1

The dimensions of the original rectangle are 5 inches by 16 inches.

Step-by-step explanation:

To find the dimensions of the original rectangle, let's assume the width of the rectangle is w. The length of the rectangle is given as 1 more than three times the width, which can be expressed as 3w + 1.

When the length is diminished by 3 inches, it becomes 3w + 1 - 3 = 3w - 2. And when the width is doubled, it becomes 2w. The perimeter of the new rectangle is given as 46 inches, so we can set up the equation:

(2w + 3w - 2) * 2 = 46

Simplifying the equation, we get 10w - 4 = 46. Solving for w, we find that the width of the original rectangle is 5 inches. Substituting this value back into the expression for the length, we can find that the length is 3(5) + 1 = 16 inches. Therefore, the dimensions of the original rectangle are 5 inches by 16 inches.