A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

the length of a rectangle box is one inch greater than its width. the height is three times the length. the diagonal box exceeds the height by one inch. Find the volume of the box.

  • This Question is Closed
  1. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1328539986535:dw|

  2. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[AB=\sqrt{w^2+(w+1)^2}=\sqrt{2w^2+2w+1)}\]

  3. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[AC=\sqrt{2w^2+2w+1+9(w+1)^2}=\sqrt{11w^2+20w+10}\]

  4. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now AC is one more than the height which is 3w+3 so AC = 3w+4

  5. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\sqrt{11w^2+20w+10}=3w+4\]

  6. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let's square both sides.

  7. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now im really confused lol

  8. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What about?

  9. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    uhhh everything lol

  10. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like idk what the main answer is lol

  11. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That might be because we haven't found the answer yet. We have to find w based on the information they gave us. Then we will be able to find the dimensions of the box and then the volume.

  12. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    As i said, let's square both sides of the equation.

  13. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[11w^2+20w+10=9w^2+24w+16\]

  14. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is 16 the square root ?

  15. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[2w^2-4w-6=0\]

  16. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Divide by 2

  17. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[w^2-2w-3=0\]

  18. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Factor

  19. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[(w-3)(w+1)=0\]

  20. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[w=3 or w=-1\]

  21. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Discard -1 since the width cannot be negative. So w = 3. That means : |dw:1328541450706:dw|

  22. Mertsj
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so the box is 3 by 4 by 12 and the volume is 3(4)(12) or 144 cubic inches

  23. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.