SOLUTION: The length of a rectangle is 3 in. more than its width. The perimeter of the rectangle is 30 in. a. Define a variable for width. b. Write and expression for the length in terms o

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Question 223704: The length of a rectangle is 3 in. more than its width. The perimeter of the rectangle is 30 in.
a. Define a variable for width.
b. Write and expression for the length in terms of width.
c. Write an equation to find the width of the rectangle. Solve your equation.
d. What is the length of the rectangle?
Found 2 solutions by rfer, drj:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
a) w
b) w+3
c) p=2w+2(w+3)
30=2w+2(w+3)
30=2w+2w+6
24=4w
w=6in
w+3=9in
d)=9in

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 3 in. more than its width. The perimeter of the rectangle is 30 in.

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

Step 2. Let w be the width.

Step 3. Let w+3 be the length.

Step 4. Then, P=w+w+w+3+w+3=4w+6=30

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: w=6.
  • Graphical form: Equation 4w%2B6=30 was fully solved.
  • Text form: 4w+6=30 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4w%2B6=30+%29
    For tutors: simplify_cartoon( 4w+6=30 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 4%2Aw%2B6=highlight_red%28+30+%29.
Moved these terms to the left highlight_green%28+-30+%29
It becomes 4%2Aw%2B6-highlight_green%28+30+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+6+%29-highlight_red%28+30+%29=0.
Added fractions or integers together
It becomes 4%2Aw%2Bhighlight_green%28+-24+%29=0.
Look at 4%2Aw%2Bhighlight_red%28+-24+%29=0.
Removed extra sign in front of -24
It becomes 4%2Aw-highlight_green%28+24+%29=0.
Look at highlight_red%28+4%2Aw-24+%29=0.
Solved linear equation highlight_red%28+4%2Aw-24=0+%29 equivalent to 4*w-24 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=6.

Universal Simplifier and Solver


Done!



With w=6 and w%2B3=9. And P=2%286%2B9%29=30 which is a true statement

Step 5. ANSWER: The width is 6 inches and the length 9 inches yards.

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