the ratio of length to breadth of a rectangular field is 4 is to 3 if its diagonal is 2200 metres, then area of the field in square metres is
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the ratio of length to breadth of a rectangular field is 4 is to 3 if its diagonal is 2200 metres, then area of the field in square metres is
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Answer:
23,23,200 Sq.m
Step-by-step explanation:
The ratio of sides of right angled triangle in this case will 3:4:5
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using Pythagoras theorem - sum of square of each side = square of hypotenuse in case of right angled triangle.
a²+b² = c² => 9x² + 16x² = 25x²
=> c = 5x
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Now
Length = 4x
Breadth = 3x
Hypotenuse = 5x
5x = 2200 m
x = 2200/5 = 440 m.
=> Length = 4* 440 = 1760 m; Breadth = 3*440 = 1320 m.
Area = L*B = 1760 * 1320 = 23,23,200 Sq.m
Step-by-step explanation:
Let ,
Length = 4x
Breadth = 3x
diagonal = 2200 m
therefore, by Pythagoras theorem
(2200)sq = (4x)sq + (3x)sq
4840000 = 16x sq + 9x sq
4840000 = 25x sq
4840000÷25= x sq
x sq = 193600
x. = 440 m
therefore,
Length = 4 × 440 = 1760m
Breadth = 3 × 440 = 1320m
Area of rectangular field = L × B
A. = 1760 × 1320
A = 2323200m sq.