Question

Use the diagram below to complete the following blanks. Inclass we observed that a2 = xc and b2 = yc. These statementscan be thought of as the areas of rectangles. Remember, thearea of a rectangle (or a square) can be found using the formulaIxw.

Answer 1

Step 1

c = x+y

`\begin{gathered} a^2=xc \\ \text{After subatitution,} \\ a^2=x(x+y) \\ a^2=x^2+xy \end{gathered}`
`\begin{gathered} b^2=yc \\ b^2=y(x+y) \\ b^2=xy+y^2 \end{gathered}`

Step 2

Square BGHC from the image has an area of

`a^2=xy\text{ + y}`