A rectangular garden is 25 feet long by 10 feet wide. You have enough mulch to cover 1000 square feet. You would like to extend both the length and the width of the garden by x feet to use up all of the mulch. Write an equation to represent the area of the new garden.
1,000 = (25 + x)(10 + x)
(25+x)(10+x) = 1000
Or, you could just double the dimensions. Then the area grows by a factor of 4, to 1000 ft^2.
Let's start by calculating the area of the original garden. The formula for the area of a rectangle is length multiplied by width.
Given:
Length (L) = 25 feet
Width (W) = 10 feet
Area (A) = L x W
Plugging in the values:
A = 25 feet x 10 feet
A = 250 square feet
Now, we want to find the area of the new garden by extending both the length and the width of the garden by x feet.
So, the new length would be (25 + x) feet, and the new width would be (10 + x) feet.
The area of the new garden would be:
(25 + x) feet x (10 + x) feet
Hence, the equation to represent the area of the new garden is:
A = (25 + x) feet x (10 + x) feet
To write an equation representing the area of the new garden, we need to consider the dimensions of the garden after extending both the length and width by x feet.
The original length of the garden is 25 feet and the original width is 10 feet. After extending both the length and width by x feet, the length will be 25 + x feet and the width will be 10 + x feet.
The area of a rectangle is given by multiplying the length by the width. So, the equation representing the area of the new garden can be written as:
Area of new garden = (25 + x) * (10 + x)
Therefore, the equation representing the area of the new garden is:
Area = (25 + x) * (10 + x)