MHB Word problem(finding dimensions)

[pita0001]

The Children at Tiny Tots Day Care plant a rectangular vegetable garden with a perimeter of 210m. The length is 3/4 the width, Find the dimensions of the garden.

I have no idea how to set up an equation. Any help is appreciated.

Would it be like 210=2(3/4+x)?

or 210=2(x-.25)?

 

[MarkFL]

You are close. Let's let $W$ be the width and $L$ be the length, and so the perimeter is:

$$210=2(L+W)$$

Now, if the length is 3/4 the width, how can we rewrite $L$ in terms of $W$?

 

[pita0001]

I don't know

210=2(L-3/4)

or 210=2(L*3/4)?

 

[MarkFL]

The statement "The length is 3/4 the width" translates into an equation as follows:

$$L=\frac{3}{4}W$$

So, substituting that into the first equation, we obtain:

$$210=2\left(\frac{3}{4}W+W \right)$$

So, now you want to solve this equation for $W$, and then use the relationship above between $L$ and $W$ to obtain the value of $L$. What do you find?

 

[pita0001]

I get 210=1.5w+2w
so W=60?
and length 45

 

[MarkFL]

I get 210=1.5w+2w
so W=60?

Yes that's correct, and so if $L$ is 3/4 of that value, what is the length?

 

[pita0001]

Length=45

thanks!:)