Question

A rectangle is twice as long as it is wide. If the length is increased by 4 cm and its width is decreased by 3 cm, the new rectangle formed has an area of 100 sq cm. Find the dimensions of the original rectangle.

Answer 1

To find the dimensions of the original rectangle, assume the width is x cm and the length is 2x cm. The width of the original rectangle is 8 cm, and the length is 16 cm.

Step-by-step explanation:

To find the dimensions of the original rectangle, let's denote the width of the rectangle as w and the length as 2w, since the rectangle is twice as long as it is wide. After increasing the length by 4 cm and decreasing the width by 3 cm, the new dimensions become (2w + 4) cm for length and (w - 3) cm for the width. The area of the new rectangle is given as 100 sq cm, which allows us to set up the equation:

• (2w + 4)(w - 3) = 100

Expanding the equation results in:

• 2w² + 4w - 6w - 12 = 100
• 2w² - 2w - 12 = 100
• 2w² - 2w - 112 = 0
• w² - w - 56 = 0

Factoring the quadratic equation:

• (w - 8)(w + 7) = 0

We find that w could be 8 or -7, but since a width cannot be negative, w must be 8 cm. Therefore, the width of the original rectangle is 8 cm and the length is 16 cm (because it's double the width).