anonymous
  • anonymous
Lenght of rectangle is 7 cm less than 4 times its width. Area is 36, find dimensions. Is this set up right? : 4x-7=36
Mathematics
schrodinger
  • schrodinger
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asnaseer
  • asnaseer
not quite - the question says that the length is 7cm less than 4 times its width, so if we call the length y and the width x, then you can write: y = 4x - 7 It also says the area is 36, so we know the area of a rectangle is length times width, therefore: xy = 36 Now you have two equations with two unknowns so you should be able to solve this to find x and y.
anonymous
  • anonymous
What do you mean by that? How can i set it up to solve?
asnaseer
  • asnaseer
substitute the expression for y from the first equation into the second equation. that will give you a quadratic equation in x to solve.

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anonymous
  • anonymous
ok be right back.. :)
anonymous
  • anonymous
is answer 165?
asnaseer
  • asnaseer
the question was asking for the dimensions of the rectangle - so you need an answer for x and y.
anonymous
  • anonymous
ok im back
asnaseer
  • asnaseer
so how did you get 165?
anonymous
  • anonymous
i put it into the top equation the area
anonymous
  • anonymous
The length of a rectanlge is 7 cm less than 4 times its width. Its area is 36, find dimensions
anonymous
  • anonymous
I put it down here to make it easier for you
asnaseer
  • asnaseer
we have two equations:\[y=4x-7\tag{a}\]and:\[xy=36\tag{b}\]if we substitute the expression for y from equation (a) into equation (b) we get:\[x(4x-7)=36\]\[4x^2-7x=36\]\[4x^2-7x-36=0\]this is a quadratic equation which you should be able to factor (or use the quadratic equation formula) to find the two possible answers for x.
anonymous
  • anonymous
do i use bottom equation to solve now :D and two ( ) are my answer? :D
asnaseer
  • asnaseer
you need to solve:\[4x^2-7x-36=0\]this will give you two possible answers for x. one will be a positive value and the other will be a negative value. since a rectangle cannot have a negative length you can reject the negative solution. you will therefore be left with one answer for x. plug this value of x back into equation (a) above to find the corresponding value for y. that will then give you the dimensions of the rectangle.
anonymous
  • anonymous
4 and -9/4? :/
asnaseer
  • asnaseer
correct values for x: now you can reject the negative value as I stated above.
anonymous
  • anonymous
so i take out negative so its only 9/4
anonymous
  • anonymous
is the answer 4 and 9?
asnaseer
  • asnaseer
no. the quadratic equation gave you two possible solutions for x. one of these was x=4 and the other was x=-9/4. since a rectangle cannot have a negative length, you can reject the solution x=-9/4. you are therefore left with x=4 as the only valid solution for the width of the rectangle. plug this value of x into equation (a) above to get the correct valid value for the length y of the rectangle.
anonymous
  • anonymous
I think i understand now but can you give me the answer? :( I wont ask again, its just this stupid program im using keeps knocking me off and giving me new questions, the server is freaking out and if i leave it sitting for awhile trying to figure it out it makes me start over, which is unfair
asnaseer
  • asnaseer
the last step is very easy - you should be able to calculate it yourself.
anonymous
  • anonymous
what do i substitute 4 into again?
asnaseer
  • asnaseer
equation (a) above
asnaseer
  • asnaseer
substitute x=4 into: y = 4x - 7
anonymous
  • anonymous
so its y=4(4)-7? gets y
asnaseer
  • asnaseer
yes
anonymous
  • anonymous
answer is 9?
anonymous
  • anonymous
4 then 9?
asnaseer
  • asnaseer
yes, so length of rectangle is 9 and width is 4
anonymous
  • anonymous
thank you :)
asnaseer
  • asnaseer
yw

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