please i need your help guys.
A rectangular cake measuring 120 cm by 72 cm is to be divided into square pieces of the same size and the largest size possible. What will be the measure of the side of each square and how many pieces will there be?
We showed you how to solve this kind of problem. Now it's your turn to show us what you've learned.
Supposing you have a 12-inch by 18-inch rectangular cake for your Noche Buena. Your mom asks you to take a slice of the cake to be given to your needy neighbor, She told you that the area of the slice should be less than half of the cake and the width should be 2 inches less than the length
To find the measure of the side of each square, we need to determine the greatest common divisor (GCD) of the length and width of the rectangular cake. The GCD represents the largest size each square can be while still dividing the cake evenly.
Step 1: Find the GCD of 120 cm and 72 cm.
To determine the GCD, we can use the Euclidean algorithm. We divide the larger number by the smaller number and take the remainder. We repeat this process until the remainder is zero. The last non-zero remainder will be the GCD.
Using the Euclidean algorithm:
120 cm ÷ 72 cm = 1, remainder 48 cm
72 cm ÷ 48 cm = 1, remainder 24 cm
48 cm ÷ 24 cm = 2, remainder 0
The GCD of 120 cm and 72 cm is 24 cm.
Step 2: The measure of the side of each square
Since the GCD is the largest size each square can be, the measure of the side of each square will be equal to the GCD. In this case, each square will have a side length of 24 cm.
Step 3: Calculate the number of squares
To find the number of squares, we divide the length of the rectangular cake by the side length of each square and multiply it by the width of the rectangular cake divided by the side length of each square.
Number of squares = (120 cm ÷ 24 cm) × (72 cm ÷ 24 cm)
Number of squares = 5 × 3
Number of squares = 15
Therefore, there will be 15 square pieces, and each square will have a side length of 24 cm.