A rectangular garden has a length of x meters and a width of (x+4) meters. Express its area as an algebraic expression.
Answer (2)
The area of a rectangle is given by A re a = l e n g t h × w i d t h .
Substitute the given length x and width x + 4 into the formula: A re a = x ( x + 4 ) .
Expand the expression: A re a = x 2 + 4 x .
The area of the rectangular garden is x 2 + 4 x .
Explanation
Understanding the Problem We are given a rectangular garden with a length of x meters and a width of ( x + 4 ) meters. Our goal is to express the area of this garden as an algebraic expression.
Area Formula The area of a rectangle is given by the formula: A re a = l e n g t h × w i d t h In our case, the length is x and the width is ( x + 4 ) .
Substitution Substituting the given values into the area formula, we get: A re a = x × ( x + 4 ) Now, we need to expand this expression.
Expansion Expanding the expression, we distribute x to both terms inside the parentheses: A re a = x × x + x × 4 A re a = x 2 + 4 x So, the area of the rectangular garden is x 2 + 4 x square meters.
Examples
Imagine you're designing a rectangular garden. You know the length is 'x' meters, and the width is 'x+4' meters. Using the algebraic expression x 2 + 4 x , you can quickly calculate the area of the garden for any value of 'x'. For example, if x = 5 meters, the area would be 5 2 + 4 ( 5 ) = 25 + 20 = 45 square meters. This helps in planning how much space you have for planting flowers or vegetables!
The area of the rectangular garden with length x meters and width ( x + 4 ) meters is expressed as x 2 + 4 x square meters. Substituting specific values for x allows for calculating the exact area. For instance, if x = 5 meters, the area is 45 square meters.
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