SOLUTION: The perimeter of a rectangle is 60cm. If the length is decreased by 5 and the width is halved, the perimeter will decrease by 20cm. What are the length and width of the original re

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Question 223774: The perimeter of a rectangle is 60cm. If the length is decreased by 5 and the width is halved, the perimeter will decrease by 20cm. What are the length and width of the original rectangle?
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
The perimeter of a rectangle is 60cm. If the length is decreased by 5 and the width is halved, the perimeter will decrease by 20cm. What are the length and width of the original rectangle?

Step 1. Perimeter P means adding up all 4 sides of a rectangle.

Step 2. Let w be the original width.

Step 3. Let L be the original length.

Step 4. Let w/2 be the width cut in half

Step 5. Let L-5 be the length reduced by 5

Step 6. Then, original perimeter P0=L+L+w+w=2L+2w=60

Step 7. Then, new perimeter or after adding 10 to both sides.

Step 8. Our linear system of equation is given in Steps 6 and 7 as




Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 2*w to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that w=10. Since , L=20.

Answer: .





With and . And and which are true statements.

Step 5. ANSWER: The width is 10 cm and the length is 20 cm.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J
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