The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 85 cm, what is the length of the diagonal?

Question

campbell_st · Answer

well let the length = l

then the width is 2l - 5

then 

85 = l (2l - 5)

distributing gives

85 = 2l^2 - 5l 

or the quadratic 

$$2l^2 - 5l - 85 = 0$$

solve the quadratic for l

anonymous · Answer

I cant seem to find the answer?

anonymous · Answer

$$Area=85cm^2$$
$$Width=(2*length)-5$$

Now the area is determined by 
$$Area=length*width$$
Which gives you:
$$85=length*(2length-5)=2length^2-5length \rightarrow 0=2length^2-5length-85$$
Solve the equation and find the length. When you have done this, just use the pythagorean formula to find the length of the diagonal.
Since the diagonal is determined by 
$$diag=\sqrt{length^2+width^2}$$
You'll just have to put your numbers in and you will get your answer.