Question

Juan is constructing a doghouse. He

needs four pieces of plywood that are
2 ft x 3 ft rectangles. He needs two
pieces of plywood that are 2 ft x 2 ft
squares. If the plywood comes in
4 ft x 8 ft sheets, what is the
minimum number of sheets of
plywood Juan will need?​

Answer 1

he needs 32 sq ft in total.....and there are 32 sq ft in one sheet.....so....he only needs one

Explanation:

Answer 2

The minimum number of sheets of plywood required are 1 sheet.

SOLUTION:

Given, Juan is constructing a doghouse.

He needs four pieces of plywood that are 2 ft x 3 ft rectangles.

He needs two pieces of plywood that are 2 ft x 2 ft squares.

If the plywood comes in 4 ft x 8 ft sheets,

We need to find the minimum number of sheets of plywood required.

Let us take a plywood sheet and cut the two squares.

Assume that two squares are side by side, then combined squares dimensions are 4 ft x 2ft.

So, after cutting the two square shapes from that plywood sheet, dimensions of plywood are 4ft x 6ft.

Now, assume that two rectangles are side by side, then combined rectangles dimensions are 4 ft x 3 ft.

And, let us add two more rectangles by the side of above combination of rectangles,

Then, whole combination of four rectangular pieces have dimensions as 4 ft x 6 ft.

We can observe that, plywood after cutting 2 squares has the same dimensions as 4 rectangular shapes.

So, we can make the 4 rectangular shapes from remaining piece of first plywood sheet.

Hence, the minimum number of sheets of plywood required are 1 sheet.