Respuesta :
Answer:
54 whole, square pieces of cake can be cut from the cake.
Step-by-step explanation:
Given:
A rectangle cake has a length of [tex]22\frac{1}{2} \ inches[/tex] and a width of 15 inches.
And the square piece of cake has side lengths [tex]2\frac{1}{2} \ inches.[/tex]
Now, to find the whole square pieces of cake that can be cut from the cake.
So, we find the area of rectangle cake first by using formula:
Length = [tex]\frac{45}{2} \ inches.[/tex]
Width = 15 inches.
[tex]Area=length\times width\\\\[/tex]
[tex]Area = \frac{45}{2} \times 15\\\\Area=337.5\ square\ inches.[/tex]
The area of cake is 337.5 square inches.
Then, to get the area of square piece of cake by using formula:
Side = [tex]\frac{5}{2} \ inches.[/tex]
[tex]Area=(side)^2\\\\Area=(\frac{5}{2} )^2\\\\Area=\frac{25}{4} \\\\Area=6.25\ square\ inches.[/tex]
The area of square piece of cake is 6.25 square inches.
Now, to get the whole square pieces of cake that can be cut from the cake by dividing the area of cake by the area of square piece of cake:
[tex]337.5\div 6.25\\\\[/tex]
[tex]=54.[/tex]
Therefore, 54 whole, square pieces of cake can be cut from the cake.
