### Home > AC > Chapter 7 > Lesson 7.3.4 > Problem7-112

7-112.

Complete each generic rectangle below and write the area as a sum and as a product.

1.  Generic Rectangleleft edge top interior top left interior top right $10xy$ left edge bottom is4 interior bottom left interior bottom right bottom edge left $3$ bottom edge right $5x$

First figure all of the dimensions of the rectangle by dividing the known area by the given side.

$10xy$ divided by $5x$ is $2y$.

 Generic Rectangleleft edge top $2y$ interior top left interior top right $10xy$ left edge bottom is4 interior bottom left interior bottom right bottom edge left $3$ bottom edge right $5x$

To show the area as a product, write the dimensions multiplied together.

$\left(2y + 4\right)\left(5x + 3\right)$

Find the areas of all of the sections by multiplying the dimensions together, then add the areas to express as a sum.

 Generic Rectangleleft edge top $2y$ interior top left interior top right $10xy$ left edge bottom is4 interior bottom left $12$ interior bottom right $20x$ bottom edge left $3$ bottom edge right $5x$

$6y + 20x + 10xy + 12$

1.  Generic Rectangleleft edge top $5$ interior top left $10x$ interior top right left edge bottom interior bottom left $4x^2$ interior bottom right bottom edge left bottom edge right $-3$

Use the same method from part (a) to solve part (b).