Question

factors and multiples: section a checkpoint 1. what are the possible side lengths of a rectangle with area 10 square units? draw an example of each possible rectangle on the grid.

Explanation:

Step 1: Recall the formula for the area of a rectangle

The area of a rectangle is given by the formula $A = l\times w$, where $A$ is the area, $l$ is the length and $w$ is the width. Here, $A = 10$ square units. So we need to find pairs of positive integers $l$ and $w$ such that $l\times w=10$.

Step 2: Find the factor pairs of 10

We start by finding the factors of 10. The factors of 10 are the numbers that divide 10 without leaving a remainder.

• When $l = 1$, then from $l\times w=10$, we have $1\times w = 10$, so $w = 10$.
• When $l=2$, then $2\times w = 10$, and $w=\frac{10}{2}=5$.
• When $l = 5$, then $5\times w=10$, and $w = \frac{10}{5}=2$.
• When $l=10$, then $10\times w = 10$, and $w=\frac{10}{10} = 1$.

For drawing the rectangles:

• For the pair (1, 10): Draw a rectangle that is 1 unit long (in terms of the grid squares) and 10 units wide (or vice - versa).
• For the pair (2, 5): Draw a rectangle that is 2 units long and 5 units wide (or vice - versa).

Answer:

The possible side - length pairs (length and width) of the rectangle with an area of 10 square units are (1, 10), (2, 5), (5, 2), (10, 1).