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03 Dec 2020, 12:00
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Difficulty:
25%
(medium)
Question Stats:
79% (01:12) correct
21%
(01:06)
wrong
based on 34
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A farmer uses 140 feet of fencing to enclose a rectangular field. If the ratio of length to width is 3 : 4, find the diagonal, in feet, of the field.
(A) 100
(B) 50
(C) 20
(D) 10
(E) cannot be determined
(A) 100
(B) 50
(C) 20
(D) 10
(E) cannot be determined
03 Dec 2020, 19:59
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Bunuel
The perimeter = 140
Taking the variable x, length = 3x and width = 4x
Perimeter = 2(l + b) = 2(3x + 4x) = 14x
14x = 140
x = 10
Length = 30 and width = 40
Length of the diagonal = \(\sqrt{l^ + b^2} = \sqrt{30^2 + 40^2} = \sqrt{2500} = 50\)
Option B
Arun Kumar
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03 Dec 2020, 20:22
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IMO B
perimeter of rectangle = 2(length + breadth) = 140
=> (length + breadth) = 140/2 = 70
also, length : breadth = 3:4
multiplying the values by 10 => length : breadth = 30:40
=> (length + breadth) = 30+40 = 70 (which satisfies the above condition)
the length, breadth and diagonal will form a right angle triangle with the length and breadth of the rectangle as the two sides and the diagonal as the the hypotenuse
by Pythagorean triplet we know the triangle is of the form: base:height:hypotenuse = 3:4:5
multiplying all the sides by 10 => (30,40,50)
=> diagonal = 50
perimeter of rectangle = 2(length + breadth) = 140
=> (length + breadth) = 140/2 = 70
also, length : breadth = 3:4
multiplying the values by 10 => length : breadth = 30:40
=> (length + breadth) = 30+40 = 70 (which satisfies the above condition)
the length, breadth and diagonal will form a right angle triangle with the length and breadth of the rectangle as the two sides and the diagonal as the the hypotenuse
by Pythagorean triplet we know the triangle is of the form: base:height:hypotenuse = 3:4:5
multiplying all the sides by 10 => (30,40,50)
=> diagonal = 50
