A poster is 25 cm taller than it is wide. It is mounted on a piece of cardboard so that there is a 5 cm border on all sides. If the area of the border alone is 1350 cm2, what are the dimensions of the poster?
A.
40 cm wide, 65 cm long
B.
43 cm wide, 68 cm long
C.
48 cm wide, 73 cm long
D.
50 cm wide, 75 cm long
2006-11-15 06:35:25 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
What are the dimensions of the poster? Let w be the width of the poster. Then w + 25 is its height.
What are the dimensions of the board? The width is w + 10 and the height is w + 35.
The area of the whole board is
(w + 10)(w + 35) = w^2 + 45 w + 350
The area of the poster is
w * (w + 25) = w^2 + 25w
The area of the border alone is
w^2 + 45 w + 350 - w^2 - 25w = 1350
20w + 350 = 1350
20w = 1000
w = 50
The answer is D.
2006-11-15 06:39:43 · answer #1 · answered by ? 6 · 0⤊ 0⤋
The best way to do this problem is to first draw yourself a picture and label everything. The poster has a width w and a height of h. the cardboard has a width of (5 + w + 5), since there is a 5 cm space on each side, and a height of (5 + h + 5). The problem tells you that the poster is 25 cm taller than it is wide, so h = w+25, so the height of the poster is (w+25) and the height of the cardboard is (5 + w + 25 + 5). Draw this part out on paper to make sure you follow me.
Next, find the area of the cardboard and the area of the poster, and substract the area of the poster from the area of the cardboard. The answer is equal to 1350.
Area of cardboard: (w+10)(w+35) = w^2 + 45w + 350
Area of poster : (w)(w+25) = w^2 + 25w
Subtract area of poster from area of cardboard:
Area of board = 1350 = 20w + 350
solve for w, which gives w = 50
h = w+25 = 50+25 = 75.
2006-11-15 06:51:04 · answer #2 · answered by romanwahoo 2 · 0⤊ 0⤋
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2016-12-17 10:37:35 · answer #3 · answered by Anonymous · 0⤊ 0⤋
c
2006-11-15 06:39:09 · answer #4 · answered by D 1 · 0⤊ 0⤋
I think it is c
2006-11-15 10:01:45 · answer #5 · answered by timing21 2 · 0⤊ 0⤋