1. A rectangular garden is to be placed so that a side of a house serves as a boundary and 150 feet of fencing material is to be used for the other three sides. If x meters is the length of the
side of the garden that is parallel to the house, express the number of square feet in the area of the garden as a function of x.
Answer:
Let A be the area of the garden in square feet, and let x be the length of the side of the garden that is parallel to the house, in meters.
Since the garden is rectangular, the area can be found using the formula A = lw, where l is the length and w is the width. The width of the garden is x meters, and the length can be found by subtracting the length of the side parallel to the house from the total length of the three sides of fencing, which is 150 feet. Since 1 meter is equal to approximately 3.28 feet, the length of the garden can be expressed as (150 – 3.28x) feet.
Therefore, the area of the garden can be expressed as a function of x using the formula:
A = (150 – 3.28*x) * x
This function represents the number of square feet in the area of the garden as a function of the length of the side of the garden that is parallel to the house.
