Question

The contractor for a new school put a rectangular garden in the courtyard. The length of this garden is 5 feet longer than its width. If this area is 414 square feet, what is the length of the rectangle?

Answer 1

To find the length of a rectangular garden with an area of 414 square feet and the length being 5 feet longer than the width, we calculate using the area formula and solving a quadratic equation to conclude that the length is 23 feet.

Step-by-step explanation:

The question asks to find the length of a rectangular garden given that the area is 414 square feet and the length is 5 feet longer than the width. To find the length, we need to set up an equation based on the area formula for rectangles, which is length times width. Let's let w represent the width of the garden. Thus, the length would be w + 5.

The area of the rectangle is given by:

• Calculate the area: A = w(w + 5)

• Substitute the given area: 414 = w(w + 5)

• Expand and solve the quadratic equation: w² + 5w - 414 = 0

• Factor the quadratic equation: (w - 18)(w + 23) = 0

• Since the width cannot be negative, we take the positive solution: w = 18 feet

• Calculate the length: Length = w + 5 = 18 + 5

Therefore, the length of the garden is 23 feet.

Answer 2

23ft

Step-by-step explanation:

Area of the rectangle = LW

L is the length

W is the width

Given

Area = 414ft²

If the length of this garden is 5 feet longer than its width, then;

L = W+5

Substitute into the formula

414 = (W+5)W

414 = W²+5W

W²+5W-414 = 0

W = -5±√5²-4(-414)/2

W = -5±√25+1656/2

W = -5±√1681/2

W = -5+41/2

W = 36/2

W = 18ft

Since L = W+5

L = 18+5

L = 23ft

Hence the length of the rectangle is 23ft