Final answer:
The width of the house is approximately 394 inches. This is calculated by converting the footprint from square yards to square feet, and then dividing by the depth of the house on the lot to find the width in feet, which is then converted to inches.
Step-by-step explanation:
The question is asking to find the width of a house given that the footprint of the house is 168 square yards. To ascertain this, we need to understand that one yard is equivalent to 3 feet. Since the area is given in square yards, first convert it to square feet by multiplying by 9 (because 1 square yard is 9 square feet). Thus, the footprint of the house in square feet is 168 yards × 9 = 1512 square feet.
Now that we have the depth at which the house is placed on the lot, we can calculate the width. We know that the lot has a depth of 166 feet, and the house is 33 feet from the front and 87 feet from the rear, adding up to a total of 33 + 87 = 120 feet. This means the remaining depth where the house sits is 166 - 120 = 46 feet. Since the area of the house footprint is 1512 square feet, the width can be calculated as width = area / depth. Therefore, the width of the house is 1512 sq ft / 46 ft.
To get the width in feet and then convert it into inches, we need to multiply by 12 (since there are 12 inches in a foot). Thus, the width in feet is 1512 / 46 = 32.87 feet (approximately), and accordingly, the width in inches is 32.87 feet × 12 = 394.4 inches. Rounding off to the nearest inch gives us a width of 394 inches.