Question

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

Answer 1

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.

Answer 2

What do you mean by that? How can i set it up to solve?

Answer 3

substitute the expression for y from the first equation into the second equation. that will give you a quadratic equation in x to solve.

Answer 4

ok be right back.. :)

Answer 5

is answer 165?

Answer 6

the question was asking for the dimensions of the rectangle - so you need an answer for x and y.

Answer 7

ok im back

Answer 8

so how did you get 165?

Answer 9

i put it into the top equation the area

Answer 10

The length of a rectanlge is 7 cm less than 4 times its width. Its area is 36, find dimensions

Answer 11

I put it down here to make it easier for you

Answer 12

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.

Answer 13

do i use bottom equation to solve now :D and two ( ) are my answer? :D

Answer 14

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.

Answer 15

4 and -9/4? :/

Answer 16

correct values for x: now you can reject the negative value as I stated above.

Answer 17

so i take out negative so its only 9/4

Answer 18

is the answer 4 and 9?

Answer 19

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.

Answer 20

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

Answer 21

the last step is very easy - you should be able to calculate it yourself.

Answer 22

what do i substitute 4 into again?

Answer 23

equation (a) above

Answer 24

substitute x=4 into:
y = 4x - 7

Answer 25

so its y=4(4)-7? gets y

Answer 26

yes

Answer 27

answer is 9?

Answer 28

4 then 9?

Answer 29

yes, so length of rectangle is 9 and width is 4

Answer 30

thank you :)

Answer 31

yw