Question

instructions solve the following problem and choose the best answer. question a rectangular flower garden has an area of 32 square feet. if the width of the garden is 4 feet less than the length, what is the perimeter, in feet, of the garden? 24 28 32 36

Explanation:

Step1: Define variables for length and width

Let the length of the garden be \( l \) feet. Then the width \( w = l - 4 \) feet (since the width is 4 feet less than the length).

Step2: Use the area formula for a rectangle

The area \( A \) of a rectangle is given by \( A = l \times w \). We know the area \( A = 32 \) square feet. Substituting \( w = l - 4 \) into the area formula, we get:

$$ l(l - 4) = 32 $$

Expanding this, we have:

$$ l^2 - 4l - 32 = 0 $$

Step3: Solve the quadratic equation

We can factor the quadratic equation \( l^2 - 4l - 32 = 0 \). We need two numbers that multiply to -32 and add to -4. The numbers are -8 and 4. So,

$$ (l - 8)(l + 4) = 0 $$

Setting each factor equal to zero gives \( l - 8 = 0 \) or \( l + 4 = 0 \). Since length cannot be negative, we take \( l = 8 \) feet.

Step4: Find the width

Now that we have the length \( l = 8 \) feet, the width \( w = l - 4 = 8 - 4 = 4 \) feet.

Step5: Calculate the perimeter

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). Substituting \( l = 8 \) and \( w = 4 \), we get:

$$ P = 2(8 + 4) = 2 \times 12 = 24 $$

Answer:

24