SOLUTION: The matting around the picture below has a uniform width. How wide is the matting if its area equals the area of the picture? Round to the nearest hundredth of an inch. (Assume x =

Algebra ->  Triangles -> SOLUTION: The matting around the picture below has a uniform width. How wide is the matting if its area equals the area of the picture? Round to the nearest hundredth of an inch. (Assume x =      Log On


   

Question 1128963: The matting around the picture below has a uniform width. How wide is the matting if its area equals the area of the picture? Round to the nearest hundredth of an inch. (Assume x = 7 in. and y = 3 in.)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
(7+2x)*(3+2x) = 2*7*3 = 42.


21 + 6x + 14x + 4x^2 = 42


4x^2 + 20x - 21 = 0.


x%5B1%2C2%5D = %28-20+%2B-+sqrt%2820%5E2+%2B+4%2A4%2A21%29%29%2F%282%2A4%29 = %28-20+%2B-+27.13%29%2F8.


Only positive root is meaningful:  x = %28-20+%2B+27.13%29%2F8 = 0.89 in.


Check.  (7+2*0.89)*(3+2*0.89) = 41.97 square inches is close enough to 42 square inches  ---->  ! Correct !

Solved.

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If you want to see many other similar solved problems with detailed explanations, look into the lessons
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
    - Cynthia Besch wants to buy a rug for a room
    - Problems on a circular pool and a walkway around it
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.