Question

You are creating a garden whose length needs to be 5 feet less than its width and has an area of 84m^2
What should the dimensions be?

Answer 1

Let's assume the width of the garden is x feet.

According to the given information, the length needs to be 5 feet less than its width. So, the length would be x - 5 feet.

We are also given that the area of the garden is 84m^2.

To calculate the area, we need to convert the length and width into the same unit. As we are given the area in square meters, we should convert the dimensions from feet to meters.

1 feet is equal to 0.3048 meters. So, the width in meters would be x * 0.3048 and the length in meters would be (x - 5) * 0.3048.

The area in square meters is equal to the product of the length and width in meters. So, we have the equation:

(x * 0.3048) * ((x - 5) * 0.3048) = 84

Simplifying, we get:

0.09290304 * (x^2 - 5x) = 84

Multiplying both sides by 0.09290304:

x^2 - 5x = 84 / 0.09290304

x^2 - 5x = 902.2

Rearranging the equation, we get:

x^2 - 5x - 902.2 = 0

We can solve this quadratic equation using factoring, completing the square, or the quadratic formula.

Using the quadratic formula:

x = (-(-5) ± √((-5)^2 - 4(1)(-902.2))) / (2(1))

x = (5 ± √(25 + 3608.8)) / 2

x = (5 ± √(3633.8)) / 2

x = (5 ± 60.237) / 2

x ≈ (5 + 60.237) / 2 or x ≈ (5 - 60.237) / 2

x ≈ 32.6185 or x ≈ -27.6185

We can't have a negative width for our garden, so the width is approximately 32.6185 feet.

Substituting this value back into the equation for the length:

Length = 32.6185 - 5 = 27.6185 feet

Therefore, the dimensions of the garden should be approximately 32.6185 feet width and 27.6185 feet length.