CPM Homework Help : AC Problem 5-58

Find the dimensions of the generic rectangle at right. Then write an equivalency statement $\left(\text{length}\cdot\text{width}=\text{area}\right)$ of the area as a product and as a sum.

Generic rectangle. Interior top left $x^2$

interior top right $-5x$

interior bottom left $3x$

interior bottom right $-15$

Hint 1:

First, find the dimensions of the rectangle.

$(x+3)$ and $(x−5)$

Hint 2:

Area $=$ (Length)(Width)

Generic rectangle left edge top $x$

interior top left $x^2$

interior top right $-5x$

left edge bottom $3$

interior
bottom left $3x$

interior
bottom
right $-15$

bottom edge left $4$ $x$

bottom edge right $-5$

Answer:

$(x+3)(x−5)=x^2−2x−15$