SOLUTION: A poster has dimensions that are 25 cm by 30 cm is surrounded by a border of uniform width. If the area of the border is 174 cm^2, find the outside perimeter of the border.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A poster has dimensions that are 25 cm by 30 cm is surrounded by a border of uniform width. If the area of the border is 174 cm^2, find the outside perimeter of the border.      Log On


   

Question 2445: A poster has dimensions that are 25 cm by 30 cm is surrounded by a border of uniform width. If the area of the border is 174 cm^2, find the outside perimeter of the border.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
draw it.
Let x = width of the border.
total area, A = area of border + area of poster
So, A = 174 + 750
A = 924
Algebraically, A = (total length)(total width)
total length = 30 + 2x
total width = 25 + 2x
so A = (30+2x)(25+2x)
A = 750 + 60x + 50x + 4x^2
A+=+4x%5E2+%2B+110x+%2B+750
So, 4x%5E2+%2B+110x+%2B+750 = 924
4x%5E2+%2B+110x+-+174+=+0
2x%5E2+%2B+55x+-+87+=+0
x = %28-55+%2B-+sqrt%2855%5E2+-+4%282%29%28-87%29%29%29%2F%282%2A2%29
x = %28-55+%2B-+sqrt%283025+%2B+696%29%29%2F%284%29

x = %28-55+%2B-+sqrt%283721%29%29%2F%284%29

x = %28-55+%2B-+61%29%2F%284%29
so x=6/4 or x=-116/2
so x=1.5, -58
So, physically, the answer is x=1.5, so total length = 33 and total width = 28
To answer the question, the perimeter = 33+28+33+28 = 122cm
jon.