By taking the quotient between the area of the quilt and the area of a single patch, we will see that she needs 432 patches.
How many patches does she need?
To get this, we need to find the quotient between the surface area of the quilt and the area of a patch.
The quilt is 6ft by 8ft, then the area is:
A = 6ft*8ft = 48ft^2
Remember that:
1ft = 12 in
1ft^2 = (12 in)^2 = 144 in^2
Then the area in square inches is:
A = 48ft^2 = 48*(144 in^2) = 6,912 in^2
Now, the patches are squares of sidelength of 4 inches, then the area of each patch is:
a = (4 in)^2 = 16 in^2
The quotient between the areas gives:
A/a = (6,912 in^2)/(16 in^2) =432
This means that Sarah needs 432 patches, so the correct option is C.
If you want to learn more about area, you can read:
https://brainly.com/question/24487155
