Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To find the dimensions of the box, namely the height and width, we will set up and solve an algebraic equation step by step.
1. Define Variables:
- Let [tex]\( w \)[/tex] represent the width of the box in centimeters.
- Let [tex]\( h \)[/tex] represent the height of the box in centimeters.
2. Write the Given Relationships:
- The perimeter of the front of the box is 44 centimeters.
- The height [tex]\( h \)[/tex] is 3 centimeters less than twice the width [tex]\( w \)[/tex].
3. Express the Height in Terms of Width:
- According to the problem, the height [tex]\( h \)[/tex] is 3 centimeters less than twice the width:
[tex]\[ h = 2w - 3 \][/tex]
4. Write the Perimeter Formula:
- The perimeter [tex]\( P \)[/tex] of the front of the box can be expressed in terms of width and height as follows:
[tex]\[ 2(w + h) = P \][/tex]
- Substituting the given perimeter [tex]\( P = 44 \)[/tex] centimeters into the equation gives:
[tex]\[ 2(w + h) = 44 \][/tex]
5. Substitute the Expression for [tex]\( h \)[/tex] into the Perimeter Formula:
- Substitute [tex]\( h = 2w - 3 \)[/tex] into the equation [tex]\( 2(w + h) = 44 \)[/tex]:
[tex]\[ 2(w + (2w - 3)) = 44 \][/tex]
6. Simplify the Equation:
- Combine like terms inside the parentheses:
[tex]\[ 2(w + 2w - 3) = 44 \][/tex]
[tex]\[ 2(3w - 3) = 44 \][/tex]
- Distribute the 2:
[tex]\[ 6w - 6 = 44 \][/tex]
7. Solve for [tex]\( w \)[/tex]:
- Add 6 to both sides of the equation:
[tex]\[ 6w - 6 + 6 = 44 + 6 \][/tex]
[tex]\[ 6w = 50 \][/tex]
- Divide both sides by 6:
[tex]\[ w = \frac{50}{6} = \frac{25}{3} \][/tex]
8. Find the Height [tex]\( h \)[/tex]:
- Use the relationship [tex]\( h = 2w - 3 \)[/tex] and substitute [tex]\( w = \frac{25}{3} \)[/tex]:
[tex]\[ h = 2\left(\frac{25}{3}\right) - 3 \][/tex]
[tex]\[ h = \frac{50}{3} - 3 \][/tex]
[tex]\[ h = \frac{50}{3} - \frac{9}{3} \][/tex]
[tex]\[ h = \frac{41}{3} \][/tex]
Thus, the width of the box is [tex]\(\frac{25}{3}\)[/tex] centimeters, and the height of the box is [tex]\(\frac{41}{3}\)[/tex] centimeters.
1. Define Variables:
- Let [tex]\( w \)[/tex] represent the width of the box in centimeters.
- Let [tex]\( h \)[/tex] represent the height of the box in centimeters.
2. Write the Given Relationships:
- The perimeter of the front of the box is 44 centimeters.
- The height [tex]\( h \)[/tex] is 3 centimeters less than twice the width [tex]\( w \)[/tex].
3. Express the Height in Terms of Width:
- According to the problem, the height [tex]\( h \)[/tex] is 3 centimeters less than twice the width:
[tex]\[ h = 2w - 3 \][/tex]
4. Write the Perimeter Formula:
- The perimeter [tex]\( P \)[/tex] of the front of the box can be expressed in terms of width and height as follows:
[tex]\[ 2(w + h) = P \][/tex]
- Substituting the given perimeter [tex]\( P = 44 \)[/tex] centimeters into the equation gives:
[tex]\[ 2(w + h) = 44 \][/tex]
5. Substitute the Expression for [tex]\( h \)[/tex] into the Perimeter Formula:
- Substitute [tex]\( h = 2w - 3 \)[/tex] into the equation [tex]\( 2(w + h) = 44 \)[/tex]:
[tex]\[ 2(w + (2w - 3)) = 44 \][/tex]
6. Simplify the Equation:
- Combine like terms inside the parentheses:
[tex]\[ 2(w + 2w - 3) = 44 \][/tex]
[tex]\[ 2(3w - 3) = 44 \][/tex]
- Distribute the 2:
[tex]\[ 6w - 6 = 44 \][/tex]
7. Solve for [tex]\( w \)[/tex]:
- Add 6 to both sides of the equation:
[tex]\[ 6w - 6 + 6 = 44 + 6 \][/tex]
[tex]\[ 6w = 50 \][/tex]
- Divide both sides by 6:
[tex]\[ w = \frac{50}{6} = \frac{25}{3} \][/tex]
8. Find the Height [tex]\( h \)[/tex]:
- Use the relationship [tex]\( h = 2w - 3 \)[/tex] and substitute [tex]\( w = \frac{25}{3} \)[/tex]:
[tex]\[ h = 2\left(\frac{25}{3}\right) - 3 \][/tex]
[tex]\[ h = \frac{50}{3} - 3 \][/tex]
[tex]\[ h = \frac{50}{3} - \frac{9}{3} \][/tex]
[tex]\[ h = \frac{41}{3} \][/tex]
Thus, the width of the box is [tex]\(\frac{25}{3}\)[/tex] centimeters, and the height of the box is [tex]\(\frac{41}{3}\)[/tex] centimeters.
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.