Question

Shoebox A and shoebox B are similar, The ratio of the length of shoebox A to the lenght of shoebox B is 2:3. The length of shoebox A is 10 inches, and it width is 6 inches. What is the perimeter of shoebox B

Answer 1

Conditions

Shoebox A and shoebox B are similar, The ratio of the length of shoebox A to the length of shoebox B is 2:3. The length of shoebox A is 10 inches, and it width is 6 inches. What is the perimeter of shoebox B

Solution

As these shoeboxes are similar, then their ratio of the length is equal to a ratio of the width.

So, the length $x$ of shoebox B is:

$$\frac{10}{2} = \frac{x}{3}$$ $$x = 15$$

And the width $y$ of shoebox B is:

$$\frac{6}{2} = \frac{y}{3}$$ $$y = 9$$

As shoebox has a rectangular form, then the perimeter is:

$$2 \cdot (9 + 15) = 48$$

**Answer: 48**