The wide and the length of a rectangle are in the ratio 2:5. If the wide of the rstangle is increases by 25%, what should be the percentage change in the length of the rectangle so that
(a) its perimeter remains unchanged?
(b) its area remains unchanged?
F.3 percentage
2012-09-13 7:35 pm
回答 (1)
2012-09-13 10:06 pm
✔ 最佳答案
(a) Let length = x , width = y.y/x = 2/5
y = 0.4x ............(1)
Let new length = z
new width = 1.25y
Original perimeter = 2(x + y)
New perimeter = 2(1.25y + z)
Perimeter is unchanged, so
2(x + y) = 2(1.25y + z)
x + y = 1.25y + z
x + 0.4x = 1.25(0.4x) + z
1.4x = 0.5x + z
z = 0.9x
So % change in length = (0.9x - x)/x = - 0.1 = decrease 10 %
(b)
Original area = xy
New area = (1.25y)z
Area is unchanged, so
xy = 1.25yz
z = 0.8x
So % change = (0.8x - x)/x = - 0.2 = decrease 20%
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