### Home > ACC6 > Chapter 8 Unit 8 > Lesson CC1: 8.1.2 > Problem8-29

8-29.

Solve each generic-rectangle puzzle. Write your answer in the form (total length)(total width) = sum of individual area parts = total area.

1.  top edge left$40$ top edge right, blank left edge top, blank interior top left, blank interior top right$180$ left edge bottom$+7$ interior bottom left, blank interior bottom right$63$

In order to solve this rectangle, it might be useful to find the length of side $A$ first. Do this using the known information, $7$ times $A$ is equal to $63$. Can you find what $A$ equals with division?

If $A$ equals $9$, can you find what side $B$ is? Use division and the knowledge that $A$ ($9$) times $B$ is equal to $180$.

$\frac{180}{9}\;=\;\textit{B}$

Once you find that $B$ is equal to $20$, you know that the total length equals $49$ and the total width equals $27$.
Can you fill in the rest of the rectangle and write your answer in the form originally provided in the instructions?

 top edge left$40$ top edge right$\color{red}A$ left edge top$\color{red}B$ interior top left, blank interior top right$180$ left edge bottom$+7$ interior bottom left, blank interior bottom right$63$

1.  top edge left$500$ top edge middle, blank top edge right blank left edge top, blank interior top left $15000$ interior top middle, blank interior top right$90$ left edge bottom$+9$ interior bottom left, blank interior bottom middle$720$ interior bottom right, blank

• Using the same strategy as part (a), find the length of sides $A, B,\text{ and }C$. With that knowledge, you will be able to find the values of $D, E,\text{ and }F$.

It would help if you found $A\text{ or }C$ first. Remember, in the final steps, these values will serve in the tens place value.

$A = 80, B = 3, \text{ and } C = 30.$

$(583)(39) = 15000 + 4500 + 2400 + 720 + 90 + 27 = 22737$

 top edge left$500$ top edge middle$\color{red}A$ top edge right$\color{red}B$ left edge top$\color{red}C$ interior top left $15000$ interior top middle blank interior top right$90$ left edge bottom$+9$ interior bottom left$\color{red}D$ interior bottom middle$720$ interior bottom right$\color{red}F$