The combined area of two square wood pallets is 45ft^2. Each side of one square pallet is twice as long as a side of the other square pallet.

Question

find the side length of each pallet and then find the area of each pallet

 

please help need answer quick 

Answer 1

Here's what we know:

A_square = s²

45 = x² + y² (or the first square plus the second square)

This means that x is the side-length of one square, and y is the side-length of the other.

2x = y

because the length of one side is twice as long as the other.

 

45 = x² + (2x)²

45 = x² + (2x)(2x)

45 = x² + 4x²

45 = 5x²

9 = x²

3 = x

 

So the length of one side is 3 ft.

y = 2 * 3

y = 6

And the length of the other is 6 ft.

 

Let's check our answer:

45 = 3 * 3 (area of one pallet) + 6 * 6 (area of the other)

45 = 9 + 36

45 = 45