## anonymous 5 years ago the area of a triange can be modeled: A(x)=x^3-1. The length is x-1. Find a polynomial to represent the width of the triangle. (the answer is x^2 + x +1 .... how do u get that?)

1. anonymous

Is this an equilateral triangle? or an arbitrary triangle?

2. watchmath

Notice that $$x^3-1=(x-1)(x^2+x+1)$$ So the width od the triangel is $$2(x^2+x+1)$$

3. anonymous

not sure why the "2" is there. $\frac{x^3-1}{x-1}=x^2+x+1$

4. watchmath

I guess area of triangle is 1/2*base*height

5. anonymous

is the length and width? can we base and sides?

6. anonymous

oops you are right. how could i doubt it?

7. anonymous

OMG I MENT RECTANGLE SRY GUYS

8. anonymous

lol well i read "rectangle' too so it must have been a subliminal message. then there is no 2!

9. anonymous

x^3−1 -------- x−1 =x^2+x+1 how is that equal to that?

10. anonymous

actually, you are just going to use the formula of the area of a rectangle which is length times width A=lw $x ^{3}-1=w(x-1)$ divide both sides by x-1 then you will get x^3−1 -------- x−1 which is equal to x^2+x+1 through factoring its gcf.