area of 4700 ft. ^2. Its perimeter is 400 ft. Write the area as a function of the length of the rectangle. Find the values of the length and width.

Question

Please help, I want to understand how to answer it, not just the answer

Answer 1

Emily,

 

Area of a rectangle is length * width

Perimeter is the distance you would walk if you go around the rectangle, it is given as l + w + l + w = 2(l +w)

 

In given case 2(l+w ) = 400 or l + w = 200 or l = 200-w

 

Also l *w = 4700

 

Substitute for length from eq 1

 

(200-w)*w = 4700

w^2 -200w +4700 = 0

 

You can solve this quadratic to get the width, which will help you calculate the length.

Answer 2

So L*W=Area right? So what the question is asking for is the value of L in terms of W and Area. Solve for L, in the following equation.

 

L*W=Area

 

After that, substitute in the values that you know (Area), and then you'll need to solve for the Width of the Rectangle. So you know that L+L+W+W=400, now you just need to get it so you have one W on one side of the equals sign. After that you can substitute what you found for W into the first equation you found. From there you can find the value of L, and once you know L, you can find W!