Question

What is the largest flag jake can draw

Answer 1

The ratio of length to width is 3/2. Let's set up equations of ratios using first the 25 cm length of the paper and then the 20 cm width:

3 25 cm
--- = ----------
2 x

Solving for x, 3x = 50 cm, and x =16 2/3 cm. This is possible, since 16 2/3 is less than the paper width 20 cm.

3 20 cm
--- = -----------
2 x

Solving for x: 3x = 40 cm; x = 40/3 cm, or x= 13 1/3 cm. This is possible, but does not make maximum use of the 20 by 30 cm paper.

Answer: the largest flag Jake can draw on the paper given is 20 cm (length) by 16 2/3 cm.

Answer 2

The largest flag that Jake can draw on the 25 cm by 20 cm sheet of paper while maintaining the 3 to 2 ratio is 30 cm long and 20 cm wide.

How to get the largest flag

Given:

Length to width ratio of the flag = 3 to 2

Dimensions of the paper = 25 cm by 20 cm

Using the ratio (x:y = 3:2):

`\(x = 3k\) (length of the flag)\\\(y = 2k\) (width of the flag)`

Given the maximum length of the paper is 25 cm:

`\(3k = 25\)\(k = (25)/(3)\)`

Now, calculate the width using the scaling factor:

`\(y = 2 * (25)/(3) = (50)/(3)\)`

However, the width cannot exceed the width of the paper (20 cm). Therefore, the largest width within the paper's constraints is 20 cm.

Using the ratio, when the width of the flag is 20 cm:

`\(x = (3)/(2) * 20 = 30\) cm`

Therefore, the largest flag that Jake can draw on the 25 cm by 20 cm sheet of paper while maintaining the 3 to 2 ratio is 30 cm long and 20 cm wide.