SOLUTION: Bobby just received an award for employee of the year and wants to frame the plaque in b) such a way as it creates a border of uniform width around the rectangular plaque. He only

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Question 1154852: Bobby just received an award for employee of the year and wants to frame the plaque in b) such a way as it creates a border of uniform width around the rectangular plaque. He only has enough material to create a total of 16 square inches in area for the border. If the plaque is 6 inches by 9 inches, how wide should the border be?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!

The area of the plaque is 9*6 = 54 in^2
add 16 in^2 the border area
Total frame area = 70 in^2
Border width = 1/2 in

Answer by ikleyn(53742) About Me  (Show Source):
You can put this solution on YOUR website!
.
Bobby just received an award for employee of the year and wants to frame the plaque in b) such a way as it creates
a border of uniform width around the rectangular plaque. He only has enough material to create a total of 16 square
inches in area for the border. If the plaque is 6 inches by 9 inches, how wide should the border be?
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        The solution in the post by @mananth is incomplete/unreadable.
        Strictly saying, an explanation absents in the @mananth's post.
        See below my complete solution. 


Let 'x' be the uniform width of the frame.

Write an equation for the frame area

    (6+2x)*(9+2x) - 6*9 = 16


Simplify

    54 + 18x + 12x + 4x^2 - 54 = 16,

    4x^2 + 30x - 16 = 0

    2x^2 + 15x - 8 = 0


Solve using the quadratic formula:  x = 1/2 or -8.

Use the positive value.


ANSWER.  The uniform width of the frame is 1/2 of an inch.

Solved.