Question

the larger rectangle is 2 times as long and 2 times as wide as the smaller rectangle.
5
10
4
8
use the drop - down menus to make each statement true.
the area of the larger rectangle is times the area of the smaller rectangle.
the perimeter of the larger rectangle is times the perimeter of the smaller rectangle.

Explanation:

Step1: Calculate area of smaller rectangle

The formula for the area of a rectangle is $A = l \times w$. For the smaller rectangle, $l = 5$ and $w = 4$. So, $A_{small} = 5 \times 4 = 20$.

Step2: Calculate area of larger rectangle

For the larger rectangle, $l = 10$ and $w = 8$. Using the area formula, $A_{large} = 10 \times 8 = 80$.

Step3: Find the ratio of areas

To find how many times the area of the larger rectangle is compared to the smaller one, we divide $A_{large}$ by $A_{small}$: $\frac{80}{20} = 4$.

Step4: Calculate perimeter of smaller rectangle

The formula for the perimeter of a rectangle is $P = 2(l + w)$. For the smaller rectangle, $P_{small} = 2(5 + 4) = 2\times9 = 18$? Wait, no, $2(5 + 4)=18$? Wait, 5 + 4 is 9, times 2 is 18? Wait, no, wait the smaller rectangle has length 5 and width 4, so perimeter is $2(5 + 4)= 18$? Wait, no, wait 5 + 4 is 9, times 2 is 18? Wait, no, let's recalculate. Wait, 5 (length) and 4 (width). So perimeter is $2\times(5 + 4) = 2\times9 = 18$? Wait, but the larger rectangle: length 10, width 8. Perimeter is $2\times(10 + 8)=2\times18 = 36$. Then the ratio of perimeters is $\frac{36}{18}=2$. Wait, maybe I made a mistake earlier. Wait, smaller rectangle: length 5, width 4. Perimeter: 2(5+4)=18. Larger rectangle: length 10, width 8. Perimeter: 2(10+8)=36. 36/18=2. So perimeter ratio is 2. And area ratio: smaller area 54=20, larger area 108=80. 80/20=4. So that's the steps.

Answer:

For the area: 4; For the perimeter: 2