Thank you for visiting The length of a rectangle is 7 8 cm more than 4 times the width If the perimeter of the rectangle is 94 6 cm. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve the problem, let's start by setting up our equations based on the information provided.
1. Define Variables:
- Let [tex]\( w \)[/tex] be the width of the rectangle.
- According to the problem, the length [tex]\( l \)[/tex] of the rectangle is 7.8 cm more than 4 times the width. So, we can express the length as:
[tex]\[
l = 4w + 7.8
\][/tex]
2. Perimeter Formula:
- The perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[
P = 2(l + w)
\][/tex]
- We are given the perimeter is 94.6 cm, so:
[tex]\[
2(l + w) = 94.6
\][/tex]
3. Substitute the Length Expression:
- Substitute the expression for [tex]\( l \)[/tex] from step 1 into the perimeter equation:
[tex]\[
2((4w + 7.8) + w) = 94.6
\][/tex]
4. Simplify the Equation:
- Combine the terms inside the parentheses:
[tex]\[
2(5w + 7.8) = 94.6
\][/tex]
5. Expand and Solve for [tex]\( w \)[/tex]:
- Expand the equation:
[tex]\[
10w + 15.6 = 94.6
\][/tex]
- Solve for [tex]\( w \)[/tex] by isolating it on one side of the equation:
[tex]\[
10w = 94.6 - 15.6
\][/tex]
[tex]\[
10w = 79
\][/tex]
[tex]\[
w = \frac{79}{10} = 7.9
\][/tex]
6. Find the Length [tex]\( l \)[/tex]:
- Use the width to find the length:
[tex]\[
l = 4w + 7.8 = 4(7.9) + 7.8
\][/tex]
[tex]\[
l = 31.6 + 7.8 = 39.4
\][/tex]
The dimensions of the rectangle are:
- Width = 7.9 cm
- Length = 39.4 cm
Therefore, the correct option is:
d. length [tex]\( = 39.4 \)[/tex] cm; width [tex]\( = 7.9 \)[/tex] cm.
1. Define Variables:
- Let [tex]\( w \)[/tex] be the width of the rectangle.
- According to the problem, the length [tex]\( l \)[/tex] of the rectangle is 7.8 cm more than 4 times the width. So, we can express the length as:
[tex]\[
l = 4w + 7.8
\][/tex]
2. Perimeter Formula:
- The perimeter [tex]\( P \)[/tex] of a rectangle is given by:
[tex]\[
P = 2(l + w)
\][/tex]
- We are given the perimeter is 94.6 cm, so:
[tex]\[
2(l + w) = 94.6
\][/tex]
3. Substitute the Length Expression:
- Substitute the expression for [tex]\( l \)[/tex] from step 1 into the perimeter equation:
[tex]\[
2((4w + 7.8) + w) = 94.6
\][/tex]
4. Simplify the Equation:
- Combine the terms inside the parentheses:
[tex]\[
2(5w + 7.8) = 94.6
\][/tex]
5. Expand and Solve for [tex]\( w \)[/tex]:
- Expand the equation:
[tex]\[
10w + 15.6 = 94.6
\][/tex]
- Solve for [tex]\( w \)[/tex] by isolating it on one side of the equation:
[tex]\[
10w = 94.6 - 15.6
\][/tex]
[tex]\[
10w = 79
\][/tex]
[tex]\[
w = \frac{79}{10} = 7.9
\][/tex]
6. Find the Length [tex]\( l \)[/tex]:
- Use the width to find the length:
[tex]\[
l = 4w + 7.8 = 4(7.9) + 7.8
\][/tex]
[tex]\[
l = 31.6 + 7.8 = 39.4
\][/tex]
The dimensions of the rectangle are:
- Width = 7.9 cm
- Length = 39.4 cm
Therefore, the correct option is:
d. length [tex]\( = 39.4 \)[/tex] cm; width [tex]\( = 7.9 \)[/tex] cm.
Thank you for reading the article The length of a rectangle is 7 8 cm more than 4 times the width If the perimeter of the rectangle is 94 6 cm. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
