Question

A rectangle has a base of 3x - 2 and a height of 3. The perimeter is 44. Find the area.

a) 90 square units
b) 92 square units
c) 94 square units
d) 96 square units

Answer 1

3x - 2 + 3 = 22

3x = 21

x = 7

Area = 3(3(7) - 2) = 3(19) = 57 square units

None of the choices are correct.

Answer 2

To calculate the area of the rectangle, we determined the value of 'x' by using the given perimeter. Solving for 'x' gave us the dimensions of the rectangle, with which we calculated the area to be 57 square units.

Step-by-step explanation:

To find the area of the rectangle, we need to first use the given perimeter to find the dimensions. The perimeter of a rectangle is calculated as P = 2×length + 2×width. Given that the base (or length) is 3x - 2 and the height (or width) is 3, the formula becomes:

44 = 2×(3x - 2) + 2×(3)

By solving this equation, we aim to find the value of 'x' which will then be used to find the area.

1. First, distribute the 2 on the right side of the equation:
2. 44 = 6x - 4 + 6
3. Combine like terms:
4. 44 = 6x + 2
5. Subtract 2 from both sides:
6. 42 = 6x
7. Divide both sides by 6:
8. 7 = x

Now that we have found 'x' to be 7, we can find the base of the rectangle:

Base = 3x - 2 = 3(7) - 2 = 21 - 2 = 19

Now, we use the formula for the area of a rectangle which is Area = length × width. In this case, the area is:

Area = (3x - 2) × 3 = 19 × 3 = 57 square units.