The surface area covered by a rectangular playground is 100 square yards. The width of the playground is 15 yards longer than its length. Using factors, find the length and the width of the playground.
Why did the rectangular playground go to therapy?
Because it was having trouble with its dimensions!
Let's go step-by-step to solve this problem.
Let's assume the length of the playground is "x" yards.
According to the problem, the width of the playground is 15 yards longer than its length.
So, the width can be represented as (x + 15) yards.
Now, we know that the surface area covered by the rectangular playground is 100 square yards.
The formula for calculating the surface area of a rectangle is length multiplied by width.
So, we have the equation:
length * width = surface area
x * (x + 15) = 100
To find the length and width, we need to solve this equation for x.
Expanding the equation gives us:
x^2 + 15x = 100
Rearranging the equation gives us:
x^2 + 15x - 100 = 0
Now, let's factorize the equation:
(x + 20)(x - 5) = 0
This gives us two possible solutions:
x + 20 = 0 --> x = -20 (Discard this negative length as it does not make sense in the context of the problem.)
x - 5 = 0 --> x = 5
Therefore, the length of the playground is 5 yards.
Since the width is 15 yards longer than the length, the width would be:
5 + 15 = 20 yards.
So, the length of the playground is 5 yards, and the width is 20 yards.
To find the length and width of the playground, we can set up an equation based on the given information.
Let's assume the length of the playground is x yards.
According to the problem, the width of the playground is 15 yards longer than its length, so the width would be x + 15 yards.
The formula for the surface area of a rectangle is length multiplied by the width.
Surface Area = Length × Width
We know that the surface area of the playground is 100 square yards. So we can write the equation as:
100 = x(x + 15)
To solve this quadratic equation, we need to factor it.
Step 1: Multiply x by x, and then by (x + 15) to get:
100 = x^2 + 15x
Step 2: Rearrange the equation as:
x^2 + 15x - 100 = 0
Now we can factor the equation.
Step 3: To factor this quadratic equation, we need to find two numbers that multiply to get -100 and add up to 15. The numbers -5 and 20 satisfy these conditions.
The factored form of the equation is:
(x - 5)(x + 20) = 0
Step 4: Set each factor equal to zero and solve for x:
x - 5 = 0 or x + 20 = 0
Solving these equations gives us two possible values for x:
x = 5 or x = -20
Since the length cannot be negative, we discard x = -20.
Therefore, the length of the playground is x = 5 yards.
To find the width, we can substitute this value back into the equation:
Width = Length + 15 = 5 + 15 = 20 yards
So, the length of the playground is 5 yards, and the width is 20 yards.
Usually the "length" of a rectangle is greater than its "width", but anyway.....
let the length be x yds
then the width is x+15 yds
x(x+15) = 100
x^2 + 15x - 100 = 0
(x - 5)(x + 20) = 0
x = 5 or x = -20, the latter is not possible
the length is 5 and the width is 20 yards