the total area of a rectangle is 70.4375. the perimeter is 36. write the dimensions of the length and the width

Question

anonymous · Answer

Call the short side of the rectangle x, and the longer side y. 

Can you think of some equations that must be satisfied.

E.g. 2x+2y=36  (this is for the perimeter)

What is the other one?

anonymous · Answer

L x W =70.4375 (equation1)
2L +2W=36 (equation2)

Solve these by simultaneous equation:)

anonymous · Answer

x X y= 70.4375

anonymous · Answer

I tried to solve for them and ended up completing the square... which did not go
 very well

anonymous · Answer

So your two equations are 

xy=70.4375  and  x+y = 18  (the same as 2x+2y=36)

So you could write x as $$x = \frac{ 70.4375 }{y  }$$

Substituting this into x+y=18 gives us

70.4375 + y^2 = 18y

y^2 - 18y + 70.4375 = 0

From here I would use the quadratic formula to get two values for y, remember this is length so we can ignore the negative answer! :)

anonymous · Answer

$$\frac{ 18+\sqrt{42.25} }{ 2 }$$

anonymous · Answer

Yeah well done, which is actually just 12.25. This is your y.

Now you can work out x by subbing that back in and you have your answer!

anonymous · Answer

ok thanks