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 expression for the area 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]
In this problem, the length and width of the rectangle are given as algebraic expressions in terms of [tex]\( x \)[/tex].
Length: [tex]\( 2x + 7 \)[/tex] feet
Width: [tex]\( 2x - 7 \)[/tex] feet
Now, let's find the expression for the area by multiplying the length by the width:
1. Write down the expressions for length and width:
- Length = [tex]\( 2x + 7 \)[/tex]
- Width = [tex]\( 2x - 7 \)[/tex]
2. Use the distributive property to multiply these binomials:
[tex]\[
(2x + 7) \times (2x - 7)
\][/tex]
3. Apply the formula [tex]\((a + b)(a - b) = a^2 - b^2\)[/tex] to simplify:
[tex]\[
a = 2x, \quad b = 7
\][/tex]
Using this formula:
[tex]\[
(2x)^2 - (7)^2 = 4x^2 - 49
\][/tex]
This final expression, [tex]\( 4x^2 - 49 \)[/tex], represents the area of the recreation space in terms of [tex]\( x \)[/tex].
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
In this problem, the length and width of the rectangle are given as algebraic expressions in terms of [tex]\( x \)[/tex].
Length: [tex]\( 2x + 7 \)[/tex] feet
Width: [tex]\( 2x - 7 \)[/tex] feet
Now, let's find the expression for the area by multiplying the length by the width:
1. Write down the expressions for length and width:
- Length = [tex]\( 2x + 7 \)[/tex]
- Width = [tex]\( 2x - 7 \)[/tex]
2. Use the distributive property to multiply these binomials:
[tex]\[
(2x + 7) \times (2x - 7)
\][/tex]
3. Apply the formula [tex]\((a + b)(a - b) = a^2 - b^2\)[/tex] to simplify:
[tex]\[
a = 2x, \quad b = 7
\][/tex]
Using this formula:
[tex]\[
(2x)^2 - (7)^2 = 4x^2 - 49
\][/tex]
This final expression, [tex]\( 4x^2 - 49 \)[/tex], represents the area of the recreation space in terms of [tex]\( x \)[/tex].
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Rewritten by : Jeany
