SOLUTION: A poster is 24 cm taller than it is wide. If it is mounted on a piece of cardboard so that there is a 6cm boarder on all sides and if the area of the boarder is 720cmsquared What

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A poster is 24 cm taller than it is wide. If it is mounted on a piece of cardboard so that there is a 6cm boarder on all sides and if the area of the boarder is 720cmsquared What       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1000286: A poster is 24 cm taller than it is wide. If it is mounted on a piece of cardboard so that there is a 6cm boarder on all sides and if the area of the boarder is 720cmsquared What are the dimensions of the poster
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Solution already posted for the IDENTICAL problem,
http://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1000131.html

That might contain a mistake but the process shown should be clear enough, so study that one, and fix what you can.

---
Using slightly different variables' assignments, here is a better solution:


t for how tall the poster, w for how wide the poster
x for uniform width of the border;
t=w+24
x=6
-
Total area is %28t%2B2x%29%2A%28w%2B2x%29
Border Area is %28t%2B2x%29%28w%2B2x%29-tw=720
STEPS
tw%2B2xw%2B2xt%2B4x%5E2-tw=720
2xw%2B2xt%2B4x%5E2-720=0
xw%2Bxt%2B2x%5E2-360=0
xw%2Bx%28w%2B24%29%2B2x%5E2-360=0
xw%2Bxw%2B2%2A24%2B2x%5E2-360=0
2xw%2B2%2A24%2B2x%5E2-360=0
xw%2B24%2Bx%5E2-360=0
xw=360-24-x%5E2
w=%28360-24-x%5E2%29%2Fx
Substitute for the assigned x=6
w=%28360-24-36%29%2F6
Evaluate w,
w=60-4-6
highlight%28w=50%29------width of poster

t=50%2B24
highlight%28t=74%29-------how tall the poster

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A poster is 24 cm taller than it is wide. If it is mounted on a piece of cardboard so that there is a 6cm boarder on all sides and if the area of the boarder is 720cmsquared What are the dimensions of the poster 
With W being width of poster, equation to form is: Area of cardboard, less area of border, equals area of poster, OR

W%5E2+%2B+48W+%2B+432+-+720+=+W%5E2+%2B+24W 

Solve this for the width, or W, to get: highlight_green%2812%29 cm

Height of poster: 12 + 24, or highlight_green%2836%29 cm