a poster is 25cm taller than it is wide. it is mounted on a piece of cardboard so that there is a 5cm border on all sides. if the area of the border alone 1350cm^2, what are the dimensions of the poster?
It is almost a must to draw a diagram but I can't do that on the computer. It will help you to do so.
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height of inside poster = w+25
width of inside poster = w
area of inside poster =w*(w+25)
Border is 5 cm on each side; therefore, its height is w+25+top5cm+bottom 5cm=w+35
Border width = w + left 5 cm + right 5 cm = w + 10 cm.
area of entire unit is (w+35)*(w+10)
area of inside poster is w*(w+25)
The border is 1350 cm2. Set this into an equation.
area entire unit-1350=area inside unit.
(w+35)*(w+10)-1350 = w(w+25)
Solve for w, which is the width of the inside poster. Add 25 to that to obtain the height. Then add 10 to each to obtain the dimensions of the entire frame. Post your work if you get stuck.
50
To find the dimensions of the poster, we can follow these steps:
1. Let's assume the width of the poster is 'w' cm.
2. Since the poster is 25 cm taller than its width, the height of the poster would be (w + 25) cm.
3. The border on each side is 5 cm, so the actual width of the poster, including the border, would be (w + 2*5) cm, which simplifies to (w + 10) cm.
4. Similarly, the actual height of the poster, including the border, would be ((w + 25) + 2*5) cm, which simplifies to (w + 35) cm.
5. The area of the border alone is given as 1350 cm².
6. We can set up an equation for the area of the entire unit (including the border) and subtract the area of the poster to get the area of the border alone: (w + 35) * (w + 10) - w * (w + 25) = 1350 cm².
- The first term, (w + 35) * (w + 10), represents the area of the entire unit (including the poster and the border).
- The second term, w * (w + 25), represents the area of the poster.
7. Simplify and solve the equation for 'w' to find the width of the poster.
8. Add 25 to the width to find the height of the poster.
9. Add 10 to the width and 35 to the height to find the dimensions of the entire frame.
By following these steps, you should be able to determine the dimensions of the poster.