Answer:
![Measurement = 0.75ft](https://img.qammunity.org/2021/formulas/mathematics/high-school/njzewepeaqwu3ylodcmmv6p09sxhcirg4v.png)
Explanation:
See attachment for complete question
Method 1:
Considering the width and length of the quilt
Given
![Number\ of\ squares = 24](https://img.qammunity.org/2021/formulas/mathematics/high-school/lrmdvqzil8w92tryqu27ne9b57mtxwc6xq.png)
Required
Determine the dimension of 1 square
The width of the quilt is 4.5ft and there are 6 squares in that dimension.
Each measurement is calculated as thus:
![Measurement = (4.5ft)/(6)](https://img.qammunity.org/2021/formulas/mathematics/high-school/pftsapqx5fgww0p61a3hysxflgq6j4nyr1.png)
![Measurement = 0.75ft](https://img.qammunity.org/2021/formulas/mathematics/high-school/njzewepeaqwu3ylodcmmv6p09sxhcirg4v.png)
Or
The length of the quilt is 3ft and there are 4 squares in that dimension.
Each measurement is calculated as thus:
![Measurement = (3ft)/(4)](https://img.qammunity.org/2021/formulas/mathematics/high-school/lmixjiss6shds61qhu94wa65izdjiypxwb.png)
![Measurement = 0.75ft](https://img.qammunity.org/2021/formulas/mathematics/high-school/njzewepeaqwu3ylodcmmv6p09sxhcirg4v.png)
Method 2:
Calculate the area of the quilt.
![Area = 4.5ft * 3ft](https://img.qammunity.org/2021/formulas/mathematics/high-school/q5c2lk9kmv2lv0f6r8bvnhljbk8q7zjeez.png)
![Area = 13.5ft^2](https://img.qammunity.org/2021/formulas/mathematics/high-school/w448d7s6ccv564vqpclhewl62kjgyhch4l.png)
The area of 1 of the 24 squares is calculated by dividing the total area by number of squares
![Area = (13.5ft^2)/(24)](https://img.qammunity.org/2021/formulas/mathematics/high-school/2ifa7swxhm0kurs8rtdbyk4hrxaaa8973u.png)
![Area = 0.5625\ ft^2](https://img.qammunity.org/2021/formulas/mathematics/high-school/wi2ynz5wstaa1egpy5c447u5bj03bokrtc.png)
Represent the dimension of individual square with L
Area of a square is:
![Area = L * L](https://img.qammunity.org/2021/formulas/mathematics/high-school/ejoutpri5oe5zg1iduy4a0qfiay57uf01c.png)
This gives:
![L * L = 0.5625](https://img.qammunity.org/2021/formulas/mathematics/high-school/7izb1vhlnqkfvqhqrc171jligqeqgpfxlq.png)
![L^2 = 0.5625](https://img.qammunity.org/2021/formulas/mathematics/high-school/ol0gs16vl45xukorlbo1cmpzu814zsewfz.png)
Take square root of both sides
![L = \sqrt{0.5625](https://img.qammunity.org/2021/formulas/mathematics/high-school/6cr9uadzv8dw2v1n1dstah34kqp5868k03.png)
![L = 0.75ft](https://img.qammunity.org/2021/formulas/mathematics/high-school/azd10pios6bxtr0lapd4p02wh1vclwyko6.png)
Hence, the dimension of each square is 0.75ft