Question

The length of a rectangle is 3 ft longer than its width.

If the perimeter of the rectangle is 42 ft, find its area.

Answer 1

To find the area of a rectangle with a given perimeter, we need to determine the width and length of the rectangle. By applying the formula for the perimeter and solving for the width, we can find the dimensions of the rectangle. Finally, we can calculate the area by multiplying the width and length.

Step-by-step explanation:

To find the area of the rectangle, we need to know the width and length of the rectangle. Let's represent the width as 'w'. According to the given information, the length is 3 feet longer than the width, so we can represent the length as 'w + 3'.

The perimeter of a rectangle is given by the formula: P = 2(w + l), where P is the perimeter, w is the width, and l is the length.

In this case, we know that the perimeter is 42 feet. Substituting the given values into the formula, we get: 42 = 2(w + (w + 3))

Simplifying the equation and solving for 'w', we find that the width is 9 feet. The length can be found by adding 3 to the width, which gives us a length of 12 feet.

The formula for the area of a rectangle is given by: A = w * l, where A is the area, w is the width, and l is the length.

Substituting the values we found, we get: A = 9 * 12 = 108 square feet.

Answer 2

A = 108 feet²

Step-by-step explanation:

Let the width is b.

Length = 3+b

Perimeter of the rectangle, P = 42 ft

Perimeter = 2(l+b)

42 = 2 (3+b+b)

21 = (3+2b)

21-3 = 2b

18 = 2b

b = 9 feet

Length, l = 3+9 = 12 feet

Area of the rectangle,

A = lb

So,

A = 12 × 9

A = 108 feet²

So, the area of the rectangle is 108 feet².