the width of a rectangle picture is one-half the length.the perimeter of the rectangle is 72 inches.find the length of the picture

Question

anonymous · Answer

the width is 1/2 the length. 
so the width would be 1/2x, while the length would be x. 
perimeter is l+l+w+w=p or in this case,
x+x+1/2x+1/2x=72
now, we solve the equation.

anonymous · Answer

You are given with:
$$Width = \frac{1}{2}Length$$
$$Perimeter = 72 \implies 2(Width + Length) = 72$$

anonymous · Answer

x=24. 
so the length is 24 while the width is 12. 

check your answer. 24+24+12+12=72 (:

anonymous · Answer

So:
$$L = 2W$$
$$2(L + W) = 72 \implies \color{green}{L + W = 36} \implies \color{red}{L + \frac{1}{2}L = 36}$$
Solve this..

gavlois1 · Answer

|dw:1365699520043:dw|

We have to set up the rectangle in this way because to be able to solve it, we need to have only one variable. By setting x as the width, the length is double it, or 2x.

Since the perimeter is the sides added up, it will end up being $$x+x+2x+2x = 72$$

After combining the terms:

$$6x = 72$$

Solve for x, and we get 12. So x = 12. However, we aren't done yet.

X was the width, but the length was 2x, so we have to double our result, so the final answer is 24 for the length.

anonymous · Answer

Or precisely:
$$\frac{3}{2}L = 36 \implies L = \frac{36 \times 2}{3} = \color{blue}{24}$$

anonymous · Answer

thank you all very helpful