8M 3 Mary will make a small 8inchby12 inch rectangular quil

8M #3 - Mary will make a small 8-inch-by-12 inch rectangular quilt for a doll house out of identical square patches. Each square patch must have side lengths that are a whole number of inches and no partial squares are allowed in the quilt. Other than using 1-inch-by-1-inch squares, what size squares can Mary use to make her quilt? Show Mary\'s options below. What are the largest squares she can use?

Solution

8x12 = 96 sq inches

we need square patches of sizes which should be a perfect square themselves and should be

factor of total area of quilt are 96 inch^2

Out of the cases we have : 96/4 = 24 ; 96/8 = 12 ; 96/12 = 8 ; 96/16 = 6 ;

Only 4 , 16 are perfect sqaures, so size of sqaure patches are 2x2 inch and 4 x4 square inches

So, these are the options available

Largest sqaure is 16 inch^2