the length of a rectangle is 3 more than 5times the width find the perimeter is area=92m^2

Question

anonymous · Answer

typo its meant to be if instead of is

imstuck · Answer

Area formula is L * W.  We have here that the Length is 3 more than 5 times the width, so the L = 5W + 3.  Multiply that by the width (W) and get this:$$A=(5W+3)(W)$$That multiplies out to $$A=5W ^{2}+3W$$We also know that A is 92, so that goes in there too:

imstuck · Answer

$$92=5W ^{2}+3W$$We have to solve that for W, and in order to do that we have to set up a quadratic equation.  Like this:

imstuck · Answer

$$5w ^{2}+3w-92=0$$That needs to be factored to find w.  Let's do that, then!

anonymous · Answer

(5w+23)(w-4)

imstuck · Answer

Ok,...but when you solve those for w what do you get?

imstuck · Answer

Very good, btw!

anonymous · Answer

-23/5, -4

imstuck · Answer

5w=-23    w= -23/5.  OR  w - 4 = 0   w = 4  We know that length cannot be a negative number so the width is 4.  Now find the length.  Do that by using your L = 5w+3.

imstuck · Answer

L=5(4)+3   L = 23.  Perimeter formula is P = 2L + 2W.  L is 23 and W is 4 so...
P = 2(23) + 2(4)   P = 46 + 8   P = 54 meters

anonymous · Answer

Thanks again