SOLUTION: A rectangle has a perimeter of 100 inches. Its length is (7x + 2) and its width is (5x). What is the value of x and find the actual measurement of the length and width.

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Question 218299: A rectangle has a perimeter of 100 inches. Its length is (7x + 2) and its width is (5x). What is the value of x and find the actual measurement of the length and width.
Found 2 solutions by solver91311, drj:
Answer by solver91311(16877) About Me  (Show Source):
You can put this solution on YOUR website!


The perimeter of a rectangle is given by:

.

Making the appropriate substitutions:



Solve for and then substitute that value back into to find the length and to find the width.


John

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle has a perimeter of 100 inches. Its length is (7x + 2) and its width is (5x). What is the value of x and find the actual measurement of the length and width.

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

Step 2. Let the Length L=7x+2 and width w=5x.

Step 3. Then, P=L%2BL%2Bw%2Bw=2%28L%2Bw%29=2%287x%2B2%2B5x%29=2%2812x%2B2%29=24x%2B4. Solving yields the following steps.

P=100=24x%2B4

Subtract 4 from both sides of the equation

100-4=24x%2B4-4

96=24x}

Divide 4 to both sides of the equation

96%2F24=24x%2F24

x=4, L=7x%2B2=7%2A4%2B2=30, w=5x=5*4=20

Check P=2%28L%2Bw%29=2%2830%2B20%29=100 which is a true statement.

Step 4. ANSWER: The answer is x=4, length is 30 inches and width is 20 inches.

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV