Question

The length of a rectangle is 4 less than 3 times its width. If its perimeter is 32, then find the area of the rectangle.

a) 30 square units
b) 36 square units
c) 40 square units
d) 48 square units

Answer 1

To find the area of the rectangle, we need to solve for width using the perimeter equation, determine the length from the given relationship, and then multiply the length by the width. The rectangle's area is found to be 55 square units.

Step-by-step explanation:

The question asks us to find the area of a rectangle given its perimeter and a relationship between its length and width. Using algebra, we can establish two equations:

Let the width be w, so the length is 3w - 4 (4 less than 3 times the width). The perimeter of a rectangle is given by P = 2l + 2w, where l is the length and w is the width. We are given that the perimeter P is 32, so:

32 = 2(3w - 4) + 2w

Solving this equation gives us the width w, and from there, we can find the length l. Once we have both the length and width, we multiply them to find the area.

Step-by-Step Solution:

1. Set up the equation for perimeter: 32 = 2(3w - 4) + 2w.
2. Solve for w: 32 = 6w - 8 + 2w, which simplifies to 8w = 40, and then w = 5.
3. Find the length l using the width: l = 3(5) - 4 = 11.
4. Calculate the area: Area = w × l = 5 × 11 = 55 square units.

Therefore, the area of the rectangle is 55 square units.