find dimensiond of rectangle

Question

area is 700sqft length is 5 feet less than twice its width find dimension 

Answer 1

Here's what we know:

A_rec = lw

A = 700

l = 2w - 5 (length is 5 less than twice width)

 

Now that we have some values, let's put them into our equation:

700 = (2w - 5)w

700 = 2w² - 5w

0 = 2w² - 5w - 700

 

Maybe we can easily factor here? Square root of 700 is a little above 26.

700 / 25 = 28

(2w ± 25)(w ± 28) Either way, the middle term is too large. Let's try something a little more disparate:

 

700 / 20 = 35

(2w + 35)(w - 20)

Here we get 35 - 40 to give us a middle term of -5, just what we need.

 

We can't have a negative length for a side, so we throw out the 2w + 35 and focus on the other:

w - 20 = 0

w = 20

 

Now that we have width, we can find length:

l = 2*20 - 5

l = 40 - 5

l = 35

 

And just as 700 / 20 = 35, 35 * 20 = 700.