Question
Clarke purchased wood chips for the new playground at Innovation Park. The rectangular playground has a width representing (3x + 5) feet and a length of (12x – 1) feet. Which expression represents the area of the playground?
Answers
GPT-4o mini
To find the area of the rectangular playground, we use the formula for the area of a rectangle, which is given by:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
In this case, the width of the playground is given as \( (3x + 5) \) feet and the length is given as \( (12x - 1) \) feet. Therefore, the area can be expressed as:
\[
\text{Area} = (12x - 1)(3x + 5)
\]
To find the expression for the area, we can use the distributive property (also known as the FOIL method for binomials):
\[
\text{Area} = (12x)(3x) + (12x)(5) + (-1)(3x) + (-1)(5)
\]
Now we calculate each term:
1. \( (12x)(3x) = 36x^2 \)
2. \( (12x)(5) = 60x \)
3. \( (-1)(3x) = -3x \)
4. \( (-1)(5) = -5 \)
Next, we combine these terms:
\[
\text{Area} = 36x^2 + 60x - 3x - 5
\]
Now, combine the like terms (\(60x - 3x\)):
\[
\text{Area} = 36x^2 + 57x - 5
\]
Thus, the expression that represents the area of the playground is:
\[
\boxed{36x^2 + 57x - 5}
\]
\[
\text{Area} = \text{Length} \times \text{Width}
\]
In this case, the width of the playground is given as \( (3x + 5) \) feet and the length is given as \( (12x - 1) \) feet. Therefore, the area can be expressed as:
\[
\text{Area} = (12x - 1)(3x + 5)
\]
To find the expression for the area, we can use the distributive property (also known as the FOIL method for binomials):
\[
\text{Area} = (12x)(3x) + (12x)(5) + (-1)(3x) + (-1)(5)
\]
Now we calculate each term:
1. \( (12x)(3x) = 36x^2 \)
2. \( (12x)(5) = 60x \)
3. \( (-1)(3x) = -3x \)
4. \( (-1)(5) = -5 \)
Next, we combine these terms:
\[
\text{Area} = 36x^2 + 60x - 3x - 5
\]
Now, combine the like terms (\(60x - 3x\)):
\[
\text{Area} = 36x^2 + 57x - 5
\]
Thus, the expression that represents the area of the playground is:
\[
\boxed{36x^2 + 57x - 5}
\]