"Question 9 A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time − (i) the length of the shadow cast by another pole 10 m 50 cm high (ii) the height of a pole which casts a shadow 5 m long.
Class 8 Direct and Inverse Proportions Page 208"
Answers
If two quantities increase or decrease together in such a manner that the ratio of their corresponding values remain constant, we say that the two quantities vary directly.
In other words x and y are said to vary directly if X/y = k , where k is a positive constant.
In direct Proportion
x/y= k
x=ky
So we can find value of k from known values, and then use the formula to calculate the unknown values.
When two quantities x and y are in direct proportion (or vary directly) they are also written as x∝y.
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Solution:
[Table is in the attachment]
Here height of the pole and length of the shadow are in direct proportion.
1m=100cm
5m 60 cm =560cm
3m 20 cm=320cm
10m 50cm=1050cm
(i). Let the length of the shadow of another pole be x.
560/320=1050/x
x×560=1050 × 320
X=(1050×320)/560
X=600 cm
X=6m
Hence,the Length of the shadow of another pole is 6m.
(ii) Let the height of the pole be ‘x’.
560/320=x/500
X×320=500×560
X=560×500/320
X=875 cm
X= 8m 75 cm
Hence, the height of the pole is 8m 75cm.
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Hope this will help you...
Answer:
Step-by-step explanation:
Height of a vertical pole = 5m60cm
Length of shadow equals 3 m200cm
(a) let the length of the shadow be "x"
They are in direct proportion
We have, x1 upon y1=x2 upon y2
3.2 upon 5.6= x upon 10.5
X=5.6×10.5 upon 3.2
X=6m