a scheme of some lawn is shown. How much time is needed to mow the entire lawn, if in half an hour 5000 mxm of lawn can be mowed?
Answers
Given : A scheme of some lawn is shown.
In half an hour 5000m² of lawn can be mowed
To Find : How much time is needed to mow the entire lawn,
Solution:
Draw DE ⊥ AB
Area of lawn = area of Δ AED + area of trapezium BCDE
area of Δ AED = (1/2) * AE * ED
AE = 50 * 2 = 100 m
ED = 50 x 5 = 250 m
area of Δ AED = (1/2) * 100 * 250 = 12500 m²
area of trapezium BCDE = (1/2) * (BC + ED) * BE
BC = 50 x 3 = 150 m
ED = 250 m
BE = 50 x 2 = 100 m
area of trapezium BCDE = (1/2) * (250 + 150) * 100 = 20000 m²
Area of lawn = 12500 + 25000 = 37500 m²
5000 m² of lawn can be mowed in 1/2 hr
=> 10000 m² of lawn can be mowed in 1 hr
37500 m² of lawn can be mowed in = (37500 / 10000) hr
= 3.75 hrs
= 3 hrs 45 mins
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How much time is needed to mow the entire lawn,
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Answer:
Draw DE perpendicular to AB
Area of ABCD= Area of triangle ADE+ Area of
Trapezium DEBC
Area of ABCD= 1/2(100*250) +1/2(250+150)*100
= 32500 meters square
Time taken to mow 32500 meters square is
= 32500/(5000*2)
= 3.25 hrs
=3hrs15 mins