Question

Hank is building a dog run for his dog. He wants the ratio of the length to the width of the dog run to be 5 : 2. If he builds the dog run so the length is 10.5 feet, which equation can be used to solve for the width, x? What is the value of x?

Answer 1

Ratio of a length to width=5/2
l:x=5:2
l/x=5/2
l=5/2*x

L=10.5 feet
10.5*2/5=x
4.2 feet is width

Answer 2

Answer:

The equation is $\\ \frac{5}{2} : \frac{10.5ft}{x}$; The value of x is 4.2ft.

Step-by-step explanation:

A ratio is like a constant that remains between two values, and we can use it to find whatever others that keep the same constant relation between them.

Hank wants a dog run that keeps a constant relation between length to the width. That is, the length must be 2.5 times to the width ( $\\ \frac{5}{2} = 2.5$ ).

So, knowing that ratio or constant, we can represent it as follows:

$\\ \frac{lenght}{width} : \frac{5}{2}$ [ 1 ]

But, it also could be expressed as the relation between the width to the length:

$\\ \frac{width}{length}:\frac{2}{5}$ [ 2 ]

He wants a lenght of 10.5ft for building a dog run for his dog, and that this new value must keep the ratio just explained [ 1 ] to the width expected.

So, the equation is:

$\\ \frac{5}{2} : \frac{10.5ft}{x}$

And we have to find the value for x that solve this equation.

However, we can use an easier way to represent this using the equation [ 2 ] for solving x :

$\\ \frac{w}{l} :\frac{2}{5} : \frac{x}{10.5ft} \\\\ x = \frac{2 * 10.5ft}{5}=4.2ft$

That is, the width must be 4.2ft to keep the ratio length to the width 5:2 ( or the ratio width to the length 2:5).

To check this answer:

$\\ \frac{length}{width} : \frac{5}{2} =2.5$

$\\ \frac{length}{width} = \frac{10.5ft}{4.2ft} = 2.5$.

$\\ \frac{width}{length} : \frac{2}{5} = 0.4$

$\\ \frac{width}{length} = \frac{4.2ft}{10.5ft} = 0.4$.