Thank you for visiting A school created a public recreation space The length of the recreation space is tex 2x 7 tex feet and the width is tex 2x. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find the area of the base of the recreation space, we need to use the formula for the area of a rectangle, which is:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
The given dimensions for the recreation space are:
- Length: [tex]\( (2x + 7) \)[/tex] feet
- Width: [tex]\( (2x - 7) \)[/tex] feet
Now, let's substitute these expressions into the area formula:
[tex]\[ \text{Area} = (2x + 7) \times (2x - 7) \][/tex]
We can recognize that this expression resembles the pattern for the difference of squares, which states that:
[tex]\[ (a + b)(a - b) = a^2 - b^2 \][/tex]
In this scenario:
- [tex]\( a = 2x \)[/tex]
- [tex]\( b = 7 \)[/tex]
Using the difference of squares, we can simplify the expression:
[tex]\[ \text{Area} = (2x)^2 - 7^2 \][/tex]
Calculating each part:
- [tex]\( (2x)^2 = 4x^2 \)[/tex]
- [tex]\( 7^2 = 49 \)[/tex]
Therefore, the expression for the area of the base is:
[tex]\[ 4x^2 - 49 \][/tex]
So, the expression for the area of the recreation space is [tex]\( 4x^2 - 49 \)[/tex] square feet.
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
The given dimensions for the recreation space are:
- Length: [tex]\( (2x + 7) \)[/tex] feet
- Width: [tex]\( (2x - 7) \)[/tex] feet
Now, let's substitute these expressions into the area formula:
[tex]\[ \text{Area} = (2x + 7) \times (2x - 7) \][/tex]
We can recognize that this expression resembles the pattern for the difference of squares, which states that:
[tex]\[ (a + b)(a - b) = a^2 - b^2 \][/tex]
In this scenario:
- [tex]\( a = 2x \)[/tex]
- [tex]\( b = 7 \)[/tex]
Using the difference of squares, we can simplify the expression:
[tex]\[ \text{Area} = (2x)^2 - 7^2 \][/tex]
Calculating each part:
- [tex]\( (2x)^2 = 4x^2 \)[/tex]
- [tex]\( 7^2 = 49 \)[/tex]
Therefore, the expression for the area of the base is:
[tex]\[ 4x^2 - 49 \][/tex]
So, the expression for the area of the recreation space is [tex]\( 4x^2 - 49 \)[/tex] square feet.
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Rewritten by : Jeany
