A sheet of plywood measures 4 feet by 8 feet. Armand wants to build a dog house using one whole sheet of plywood for the floor.
a. Armand needs to put a "2 by 4" under the outer edges all the way around the floor, and another "2 by 4" that runs down the middle lengthwise, to give support to the plywood. If "2 by 4" are sold in 8-foot lengths, how many should he buy? __________
b. If he carpets the floor also, how many squares feet of carpet should he buy? ____________________
a) Three 8 foot long 2x4's will run lengthwise down the long sides and the middle. One more 2x4 can be sawn in half for the front and rear 4-foot edges.
That adds up to four.
b) You know the floor area is 32 square feet. That should tell you something
a. To find out how many 2 by 4s Armand needs to buy, we need to calculate the perimeter of the plywood floor. The perimeter is the sum of all the sides of the rectangle.
Perimeter = 2(length + width)
Given that the length of the plywood is 8 feet and the width is 4 feet, we can substitute these values into the formula:
Perimeter = 2(8 + 4)
Perimeter = 2(12)
Perimeter = 24 feet
Since the 2 by 4s are sold in 8-foot lengths, Armand will need to buy enough for the total perimeter, which is 24 feet. Therefore, he should buy 3 pieces of 2 by 4.
b. To calculate the number of square feet of carpet, we need to find the area of the plywood floor. The area of a rectangle is calculated by multiplying the length by the width.
Area = length * width
Area = 8 * 4
Area = 32 square feet
Therefore, Armand should buy 32 square feet of carpet to cover the floor of the dog house.
a. To determine how many "2 by 4" Armand needs to buy, we need to calculate the perimeter of the floor and the length of the additional support in the middle.
The perimeter of the floor can be calculated by adding the lengths of all four sides:
Perimeter = 2 × (Length + Width)
Given that the plywood measures 4 feet by 8 feet, the perimeter is:
Perimeter = 2 × (4 + 8) = 2 × 12 = 24 feet
Since Armand wants to put a "2 by 4" all the way around the floor, he needs to buy enough "2 by 4" to cover the perimeter. However, since "2 by 4" are sold in 8-foot lengths, he needs to round up to the nearest whole number.
Therefore, he should buy 24 feet ÷ 8 feet = 3 "2 by 4" pieces to cover the outer edges.
For the additional support in the middle, Armand needs a "2 by 4" that runs down the length of the floor. Since the length is 8 feet, he needs an 8-foot "2 by 4".
In total, he should buy 3 + 1 = 4 "2 by 4" pieces.
b. To determine how many square feet of carpet Armand should buy, we need to find the area of the floor.
The area of a rectangle can be calculated by multiplying the length and width:
Area = Length × Width
Given that the dimensions of the plywood sheet are 4 feet by 8 feet, the area of the floor is:
Area = 4 feet × 8 feet = 32 square feet
Therefore, Armand should buy 32 square feet of carpet to cover the floor.