The Carlson family is building a house on a lot that is 91 feet long and 158 feet wide.
A. Town law states that the sides of a house can't be closer than 10 ft to the edges of a lot. Write an inequality for the possible lengths of the Carlson family's house
B.The Carlson family wants their house to be at least 2800 square feet and more than 3200 square feet. They also wanted their house to have the max possible length. Write an inequality for the possible widths o f their.
do you mean, "and NO more than 3200"?
No more than * yes
I need help on this too
A. To find the possible lengths of the Carlson family's house, we need to consider the constraint given by the town law, which states that the sides of a house cannot be closer than 10 feet to the edges of the lot.
Let's assume the length of the house is represented by the variable L. According to the constraint, the distance from each side of the house to the edge of the lot should be greater than or equal to 10 feet. Since there are two sides of the house parallel to the length, we double the value of 10 to account for both sides.
Therefore, the inequality for the possible lengths of the house can be written as:
L + 2(10) ≤ 91
Simplifying the equation, we have:
L + 20 ≤ 91
B. Similarly, to find the possible widths of the Carlson family's house, we need to consider their requirements. They want the house to be at least 2800 square feet and more than 3200 square feet. The width is represented by the variable W.
The area of a rectangular house is calculated by multiplying its length by its width, so we have:
L * W ≥ 2800 (minimum requirement)
L * W > 3200 (additional requirement)
Since the Carlson family also wants the house to have the maximum possible length, we need an inequality to represent the maximum value of L. However, the length has already been constrained by the town law in part A, so we have already considered the maximum possible length (91 ft).
Therefore, the inequality for the possible widths of the house can be written as:
L * W ≥ 2800
L * W > 3200