Question

A boat maker wanted to build a canoe 6 ft long and 2 1/2 wide but decided that those dimensions were too small. The boat maker wants to add 2 ft to both the length and width but also wants to keep the canoe the same shape. Explain why this will not work.

Answer 1

Answer:

No, does not form a proportion

Step-by-step explanation:

Consider the provided information.

The length of boat was 6 ft long and 2 1/2 ft wide.

Note: 2 1/2 = 2.5

The dimensions were too small so boat maker wants to add 2 ft to both the length and width but also wants to keep the canoe the same shape.

To be the same shape the ratio should form a proportion if you add 2 ft to both the length and width.

Add 2 in length and width.

New length 6+2= 8

New width 2.5 + 2 = 4.5

Now compare the ratio as shown:

$\frac{6}{2.5}=\frac{8}{4.5}\\\\ 2.4=1.778$

Which is not true

Hence, it will not work because it does not form a proportion.

Answer 2

The ratio of length to width would change slightly, before adding on to the dimensions, the ratio is 6 : 2.5    with the added dimensions, the ratio would change to 8 : 4.5    with simple math you can see that 2.5 is less then half of 6 while 4.5 is more then half of 8