Question

Colleen and Caroline each built a rectangle out of square tiles placed in 3 rows of 5. Colleen used tiles that measured 1 2/3 cm in length. Caroline used tiles that measured 3 1/3 cm in length.

a. Draw the girls’ rectangles, and label the lengths and widths of each.
b. What are the areas of the rectangles in square centimeters?
c. Compare the areas of the rectangles.

Answer 1

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
`1(2)/(3)` cm in length.

Caroline used the tiles measuring
`3(1)/(3)` cm in length

a). We can see the figure attached.

b). Area of one tile used by Colleen = (side)²

=
`((5)/(3))^(2)=(25)/(9)` cm²

Now area of the rectangle formed =
`(25)/(9)* 15`

=
`(375)/(9)`

=
`(125)/(3)`

=
`41(2)/(3)`cm²

Area of the tile used by Caroline =
`((10)/(3))^(2)=(100)/(9)`

Since she used 15 tiles so the area of rectangle formed =
`(100* 15)/(9)`

=
`(1500)/(9)`

=
`(500)/(3)`

=
`166(2)/(3)` cm²

c). Now ratio of both the rectangles =
`\frac{\text{Colleen}}{\text{Caroline}}= ((125)/(3) )/((500)/(3) )`

=
`(125)/(500)`

=
`(1)/(4)`

Therefore ratio of the rectangles formed by Colleen and Caroline is 1 : 4