SOLUTION: a 15-inch by 28-inch poster is to be framed using a border of uniform width. to make the framing visually appealing, the border should have an area equal to 60% of the area of the

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Question 268741: a 15-inch by 28-inch poster is to be framed using a border of uniform width. to make the framing visually appealing, the border should have an area equal to 60% of the area of the poster. how wide should the border be?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a 15-inch by 28-inch poster is to be framed using a border of uniform width.
to make the framing visually appealing, the border should have an area equal to 60% of the area of the poster.
how wide should the border be?
:
Let x = the width of the border
:
Find the area of the poster:
15 * 28 = 420 sq/in
:
Find the area of the border
.6(420) = 252 sq/in
:
The overall dimensions of poster and border:
(2x+15) by (2x+28)
:
Overall area - poster area = border area
(2x+15)*(2x+28) - 420 = 252
FOIL
(4x^2 + 56x + 30x + 420) - 420 = 252
:
4x^2 + 86x + 420 - 420 = 252
:
4x^2 + 86x - 252 = 0; a quadratic equation
:
Use the quadratic formula to find the positive solution for x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: a=4; b=86; c=-252
x+=+%28-86+%2B-+sqrt%2886%5E2-4%2A4%2A-252+%29%29%2F%282%2A4%29+
:
x+=+%28-86+%2B-+sqrt%287396+-+%28-4032%29+%29%29%2F8+
:
x+=+%28-86+%2B-+sqrt%287396+%2B+4032+%29%29%2F8+
:
x+=+%28-86+%2B-+sqrt%2811428+%29%29%2F8+
:
x+=+%28-86+%2B+106.9%29%2F8+
:
x = 20.9%2F8
x = 2.61 inches is the width of the border
:
:
You can check solution:
(15+5.22)*(28+5.22) - 420 = should equal 60% of 420