A rectangular garden, with length twice its width, is to be expanded so that each side is increased by 4 yards.
a. Write expressions for the dimensions of the expanded garden.
b. Write and simplify an expression to represent the area of the expanded garden.
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If x = width, then 2x = length.
a. (x+4) by (2x+4)
b. (x+4)(2x+4)= Area
I'll let you simplify it.
a. Let's say the width of the rectangular garden is x yards. Since the length of the garden is twice its width, the length would be 2x yards.
When each side of the garden is increased by 4 yards, the new width would be x + 4 yards. Similarly, the new length would be 2x + 4 yards.
Therefore, the dimensions of the expanded garden would be (x + 4) yards for the width and (2x + 4) yards for the length.
b. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the expanded garden would be:
Area = (x + 4)(2x + 4)
To simplify this expression, we can apply the distributive property:
Area = 2x^2 + 4x + 8x + 16
Combining like terms:
Area = 2x^2 + 12x + 16
So, the simplified expression for the area of the expanded garden is 2x^2 + 12x + 16 square yards.
To solve this problem, let's break it down step by step:
a. Write expressions for the dimensions of the expanded garden:
Let's assume the width of the original rectangular garden is "x" yards.
According to the given information, the length is twice the width, so the length would be 2x yards.
When the garden is expanded, each side is increased by 4 yards. So, the new width would be (x + 4) yards, and the new length would be (2x + 4) yards.
Therefore, the expressions for the dimensions of the expanded garden are:
Width: x + 4 yards
Length: 2x + 4 yards
b. Write and simplify an expression to represent the area of the expanded garden:
The area of a rectangle is calculated by multiplying the length by the width.
So, the area of the expanded garden would be:
Area = (width of the expanded garden) * (length of the expanded garden)
Area = (x + 4) * (2x + 4)
To simplify this expression, we need to distribute the terms:
Area = 2x^2 + 4x + 8x + 16
Area = 2x^2 + 12x + 16
Therefore, the simplified expression to represent the area of the expanded garden is:
Area = 2x^2 + 12x + 16