Question

A rectangular garden has an area of 100 square meters. The length of the garden is 10 meters more than the width. What is the perimeter of the garden?

Answer 1

Let's start by using algebra to solve for the width of the garden:

- Let w be the width of the garden.

- Then the length of the garden is w + 10.

- The area of the garden is length x width, so we can write the equation: (w + 10)w = 100.

- Expanding the left side of the equation, we get: w^2 + 10w = 100.

- Rearranging the equation, we get: w^2 + 10w - 100 = 0.

- Factoring the left side of the equation, we get: (w + 20)(w - 10) = 0.

- Solving for w, we get: w = -20 or w = 10. Since the width cannot be negative, we have w = 10.

Now that we know the width of the garden is 10 meters, we can find the length by adding 10 meters:

- Length = width + 10 = 10 + 10 = 20 meters.

Finally, we can find the perimeter of the garden by adding up the lengths of all four sides:

- Perimeter = 2(length + width) = 2(20 + 10) = 2(30) = 60 meters.

Therefore, the perimeter of the garden is 60 meters.

Answer 2

40 meters

Explanation:

Let's assume the width of the garden is x meters, then the length of the garden would be (x+10) meters since we know that the length is 10 meters more than the width.

We also know that the area of the garden is 100 square meters, therefore:

Area = Length x Width

100 = (x+10) x x

Expanding the equation we get:

100 = x^2 + 10x

Rearranging the terms we have:

x^2 + 10x - 100 = 0

Solving for x using the quadratic formula, we get:

x = 5 or x = -20

Since the width cannot be negative, we discard the negative solution and conclude that the width of the garden is 5 meters. Therefore, the length of the garden is (5+10) = 15 meters.

The perimeter of the garden is the sum of the four sides, which is:

Perimeter = 2 x (Length + Width)

Perimeter = 2 x (15 + 5)

Perimeter = 2 x 20

Perimeter = 40 meters

Therefore, the perimeter of the garden is 40 meters.