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) About Me  (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 P1=L-5%2BL-5%2Bw%2F2%2Bw%2F2=2L%2Bw-10=60-20=40 or 2L%2Bw=50 after adding 10 to both sides.

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

2L%2B2w=60
2L%2Bw=50

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++2%5CL+%2B+2%5Cw+=+60%2C%0D%0A++++2%5CL+%2B+1%5Cw+=+50+%29%0D%0A++We'll use substitution. After moving 2*w to the right, we get:
2%2AL+=+60+-+2%2Aw, or L+=+60%2F2+-+2%2Aw%2F2. Substitute that
into another equation:
2%2A%2860%2F2+-+2%2Aw%2F2%29+%2B+1%5Cw+=+50 and simplify: So, we know that w=10. Since L+=+60%2F2+-+2%2Aw%2F2, L=20.

Answer: system%28+L=20%2C+w=10+%29.





With L=20 and w=10. And P0=2%2820%2B10%29=60 and P1=+2%2A20%2B10-10=40 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.

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Good luck in your studies!

Respectfully,
Dr J