Bryant Weber
04/14/2024 · Elementary School
\( 1 \leftarrow \) The perimeter of a rectangle is 600 yards. What are the dimensions of the rectangle if the length is 10 yards more than the width? The length is \( \square \) yards and the width is yards.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve this problem, we can use the formula for the perimeter of a rectangle, which is \( P = 2l + 2w \), where \( P \) is the perimeter, \( l \) is the length, and \( w \) is the width.
Given that the perimeter \( P \) is 600 yards and the length \( l \) is 10 yards more than the width \( w \), we can write the following equations:
1. \( P = 2l + 2w \)
2. \( l = w + 10 \)
Substitute the second equation into the first equation:
\( 600 = 2(w + 10) + 2w \)
Now, let's solve for \( w \):
\( 600 = 2w + 20 + 2w \)
\( 600 = 4w + 20 \)
\( 600 - 20 = 4w \)
\( 580 = 4w \)
\( w = \frac{580}{4} \)
\( w = 145 \)
Now that we have the width, we can find the length by adding 10 yards to the width:
\( l = w + 10 \)
\( l = 145 + 10 \)
\( l = 155 \)
So, the dimensions of the rectangle are:
The length is \( 155 \) yards and the width is \( 145 \) yards.
Quick Answer
The length is 155 yards and the width is 145 yards.
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit