Question

The perimeter of a rectangular garden is 46 meters, and the length is 8 meters longer than the width. Solve for the length and the width of the garden. Then find the area of the garden.

a) Length = 27 m, Width = 19 m, Area = 513 m²
b) Length = 19 m, Width = 27 m, Area = 513 m²
c) Length = 12 m, Width = 20 m, Area = 240 m²
d) Length = 20 m, Width = 12 m, Area = 240 m²

Answer 1

To solve for the length and width of the rectangular garden, we can set up two equations based on the given information. The width of the garden is 7.5 meters and the length is 15.5 meters. The area of the garden is 116.25 square meters.

Step-by-step explanation:

To solve this problem, we can set up two equations based on the given information. Let's say the width of the rectangular garden is 'w' meters. According to the problem, the length is 8 meters longer than the width, so the length is 'w + 8' meters. The perimeter of a rectangle is given by the formula: 2 * (length + width). So, we can write the equation: 2 * (w + 8 + w) = 46.

Simplifying the equation, we get: 4w + 16 = 46. Subtracting 16 from both sides, we get: 4w = 30. Dividing both sides by 4, we get: w = 7.5. So, the width of the garden is 7.5 meters and the length is 7.5 + 8 = 15.5 meters. The area of a rectangle is given by the formula: length * width. So, the area of the garden is: 15.5 * 7.5 = 116.25 square meters.