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:  

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.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

no one knows lol

step-by-step explanation: