## allie_bear22 2 years ago check my answer! Which ratio represents the area of the smaller rectangle compared to the area of the larger rectangle? (Figure not drawn to scale)

1. allie_bear22

2. allie_bear22

i got 1/4(x+2)

3. whpalmer4

That's correct.

4. allie_bear22

thnk u

5. Luigi0210

You sure it's not 4/x+2?

6. allie_bear22

hmm thats not an option but 4x(x+2) is

7. Luigi0210

$\frac{ x }{ x+5 }=\frac{ 4*(x) }{ (x+2)*(x+5) }$

8. allie_bear22

is it x/x+2?

9. Luigi0210

Hm, actually nevermind sorry.

10. allie_bear22

lol okay so the other guy was right?

11. Luigi0210

I'm not 100% sure but I'll have to take his word for it

12. allie_bear22

ok thnk u

13. whpalmer4

Area of the smaller rectangle = $$x(x+5)$$ Area of the larger rectangle = $$4x(x^2+7x+10) = 4x(x+2)(x+5)$$ Ratio of areas (smaller to larger) = $\frac{x(x+5)}{4x(x+2)(x+5)} = \frac{x}{4x(x+2)} = \frac{1}{4(x+2)}$

14. whpalmer4

@Luigi0210 was taking the ratio of the sides of the small rectangle and comparing it to the ratio of the sides of the large rectangle, which is not what problem asks....that would be the right setup for determining if the rectangles were proportional in shape, however.

15. whpalmer4

Gotta watch out, multiple-choice questions often have wrong answers that represent results you could get if you set up the problem incorrectly. Don't assume the answer is right just because it is one of the choices :-)

16. Luigi0210

Yup, I realized that right when I lef

17. Luigi0210

*left