## anonymous 3 years ago word problem!! A parcel of land is 6ft longer than it is wide. Each diagonal from one corner to the opposite corner is 174 ft long. What are the dimensions of the parcel?

1. anonymous

Draw a picture. That will help you figure out what to do.

2. anonymous

|dw:1377832287651:dw|

3. anonymous

thanks but how do I solve it?

4. anonymous

It is 6 feet longer than it is wide, so you can write an expression for both the length and the width.

5. anonymous

okay.... i did that... then what?:)

6. anonymous

Use the Pythagorean theorem.

7. anonymous

|dw:1377832617688:dw|

8. anonymous

so... (w+6)^2+w^2=174^2??????

9. anonymous

Exactly.

10. anonymous

Solve for w.

11. anonymous

okay i will tryyyy

12. anonymous

You can do it! I have faith in you!!

13. anonymous

i was trying to solve for w but i got stuck... will someone help me and walk me through it??

14. anonymous

15. anonymous

(w+6)^2+w^2=30276..... w^2+12w+36+w^2=30276......2w^2+12w+36=30267

16. anonymous

and now im stuck

17. anonymous

i was trying to use the quadratic formula but i wasnt sure what to do and my numbers were wayyyyyy big

18. anonymous

Great job! Find a calculator, you are going to need it. :-) The quadratic formula is what you will need. I'm still working through it. Before you get to that, get all terms to the left side of the equation and set it equal to 0.

19. anonymous

The numbers do get big, but you can handle it, with your calculator's help.

20. anonymous

when i do the quadratic inside the root is negative so how would i simplify it??? isnt the quadratic formula -b plus or minus the root of b^2-4ac all over 2a

21. anonymous

It is not negative. You dropped a negative on the floor....look around, I'm sure it is still nearby. :-)

22. anonymous

One you get all the terms to the left side, the constant term will be negative.

23. anonymous

I divided the whole equation by 2 to keep the numbers smaller. $$w^2+6w-15120$$

24. anonymous

but when you put in -15120 it is negative in the root soo it wont workkk

25. anonymous

the answer in the back of the book is 120 by 126

26. anonymous

so still not sure how that works when what ever i root comes out to be a decimal

27. anonymous

The answer in the back of the book is correct. $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ $w^2+6w-15120$ $\dfrac{-6 \pm \sqrt{6^2-4(1)(-15120}}{2(1)}$ remember that a negative times a negative is a positive.

28. anonymous

wow thanks soooo mcuh!! you are AMAZZZZINNNGGG!!!!

29. anonymous