Question

The length of a rectangular garden is 4 feet longer than the width. If the perimeter is 192 feet, what is the area of the garden?

Do not include units in your answer.

Answer 1

To solve for the area of the garden, we first determined the width (46 feet) by solving the perimeter equation, then we found the length by adding 4 feet to the width, resulting in 50 feet. With both dimensions, we calculated the area to be 2300 square feet.

Step-by-step explanation:

To find the area of a rectangular garden where the length is 4 feet longer than the width and the perimeter is 192 feet, we use algebra. Let's define the width of the garden as 'w' feet. Therefore, the length will be 'w + 4' feet. The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where 'l' is the length and 'w' is the width. Plugging in the known values, we get 192 = 2(w + 4) + 2w.

Simplifying that equation:

• 192 = 2w + 8 + 2w
• 192 = 4w + 8
• 184 = 4w
• w = 46 feet

Now that we have the width, we can find the length: l = w + 4 = 46 + 4 = 50 feet.

The area (A) of a rectangle is given by the formula A = l × w. Therefore, the area of the garden is:

• A = 50 × 46 = 2300 square feet

Answer 2

Given : The length of a rectangular garden is 4 feet longer than the width. If the perimeter is 192 feet, what is the area of the garden ?

Solution :

Let us assume the breadth be x

The length is 4 ft longer than the Breadth

So, the length be x + 4

Perimeter = 192

❍ Perimeter = 2(Length + Breadth)

• 192 = 2(x + 4 + x)

• 192 = 2(2x + 4)

• 192 = 4x + 8

• 192 - 8 = 4x

• 4x = 184

• x = 46

Length : x + 4 = 46 + 4 = 50

Breadth : x = 46