Answer:
Step-by-step explanation:
Colleen and Caroline each built a rectangle out of tiles placed in 3 rows of 5 tiles.
That means Both used total number of tiles = 3×5 = 15
Colleen used tiles that measured [tex]1\frac{2}{3}[/tex] cm in length.
Caroline used the tiles measuring [tex]3\frac{1}{3}[/tex] cm in length
a). We can see the figure attached.
b). Area of one tile used by Colleen = (side)²
= [tex](\frac{5}{3})^{2}=\frac{25}{9}[/tex] cm²
Now area of the rectangle formed = [tex]\frac{25}{9}\times 15[/tex]
= [tex]\frac{375}{9}[/tex]
= [tex]\frac{125}{3}[/tex]
= [tex]41\frac{2}{3}[/tex]cm²
Area of the tile used by Caroline = [tex](\frac{10}{3})^{2}=\frac{100}{9}[/tex]
Since she used 15 tiles so the area of rectangle formed = [tex]\frac{100\times 15}{9}[/tex]
= [tex]\frac{1500}{9}[/tex]
= [tex]\frac{500}{3}[/tex]
= [tex]166\frac{2}{3}[/tex] cm²
c). Now ratio of both the rectangles = [tex]\frac{\text{Colleen}}{\text{Caroline}}= \frac{\frac{125}{3} }{\frac{500}{3} }[/tex]
= [tex]\frac{125}{500}[/tex]
= [tex]\frac{1}{4}[/tex]
Therefore ratio of the rectangles formed by Colleen and Caroline is 1 : 4
