Question

Chantel is carpeting a room that has an area of x^2-100 square feet. If the width of the room is x-10 feet, what is the length of the room.

Answer 1

Here's what i've done so far:

-x+10+x^2-100= l(x-10)-x+10

(-x+10)+(x^2-100)=l

x^2-x-90=l

WHAT NEXT?

Answer 2

I don't understand your work at all.

All you have to do is divide the area by the width.

Answer 3

so that would just give me the length?

Answer 4

yes, just divide (x^2-100) by x-10
can u divide it?

Answer 5

length x width = area

is it not? 5th grade stuff.

Answer 6

ok. one sec

Answer 7

but 100/10 is 10. but then how do i divide x^2 by x?

Answer 8

exponent laws, what happens when you divide identical bases with different exponents?

Answer 9

thats not the way to divide polynomials....
wait i will give you a better approach than dividing like that....
do u know the formula:
\[a ^{2}-b^{2}=(a+b)(a-b)\]

Answer 10

yeah

Answer 11

so u can write this :
\[x^2-100 = x^2-10^2 = (x+10)(x-10)= AREA\]
got this?

Answer 12

right

Answer 13

now using this : AREA=WIDTH *LENGTH,can i write :
\[(x+10)(x-10)= (x-10) *LENGTH\]
so what will be lenght??

Answer 14

ok. one sec

Answer 15

You know that
Area=Length x Height
(x^2-100)=(x-10)( Height )
\[(Height)=\frac{(x^2-100)}{(x-10)}\]
Factoring \(x^2-100\),
\[(Height)=\frac{(x+10)(x-10)}{(x-10)}\]
\[(Height)=\frac{(x+10)\cancel{(x-10)}}{\cancel{(x-10)}}\]
\[(Height)=x+10\]

Answer 16

hartnn, to solve (x+10)(x-10) i use FOIL, right. i got x^2-100.

Answer 17

@Amenah , yes because
Area= (x+10)(x-10)
Area=x^2-100
So you're right

Answer 18

see @.Sam. comment,it explains everything in one place

Answer 19

k

Answer 20

ask if u still have doubts.....

Answer 21

for the length, i got x+10

Answer 22

yes,correct...thats your answer....understood all steps clearly?

Answer 23

yep. thank you so much! i had so many question on this packet, and now i'm almost done! can i ask you one more question?

Answer 24

ask as many as u want....