A pennant has a length-to-width ratio of 5:3. What is the length and width of the largest pennant that can be cut from a piece of cloth measuring 50 cm by 36 cm?
5:3 = 50:30
so, even using the whole 50cm length, the pennant can only be 30cm wide
To use the whole 36cm width, you'd need a 60cm length, since 5:3 = 60:36
To find the length and width of the largest pennant that can be cut from a piece of cloth measuring 50 cm by 36 cm, we need to determine the dimensions that satisfy the given length-to-width ratio of 5:3 while also considering the size of the cloth.
Step 1: Calculate the length and width based on the length-to-width ratio:
Let's assume the length of the pennant is 5x and the width is 3x (where x is a common factor). So, we have:
Length = 5x
Width = 3x
Step 2: Consider the size of the cloth:
The cloth has dimensions of 50 cm by 36 cm. We need to ensure that the dimensions of the pennant do not exceed the dimensions of the cloth.
Length: 5x ≤ 50
Solve for x:
5x ≤ 50
x ≤ 10
Width: 3x ≤ 36
Solve for x:
3x ≤ 36
x ≤ 12
Step 3: Find the maximum possible x:
To find the maximum value of x that satisfies both inequalities, we take the smaller value between x ≤ 10 and x ≤ 12.
Maximum x = min(10, 12) = 10
Step 4: Calculate the length and width of the largest pennant:
Using x = 10, we can now calculate the dimensions of the largest pennant.
Length = 5x = 5 * 10 = 50 cm
Width = 3x = 3 * 10 = 30 cm
Therefore, the length and width of the largest pennant that can be cut from the given piece of cloth are 50 cm and 30 cm, respectively.