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A farmer uses 140 feet of fencing to enclose a rectangular field. If

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Bunuel
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A farmer uses 140 feet of fencing to enclose a rectangular field. If [#permalink] New post   03 Dec 2020, 12:00
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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
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A farmer uses 140 feet of fencing to enclose a rectangular field. If [#permalink] New post   03 Dec 2020, 19:59
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Bunuel wrote:
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



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

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Re: A farmer uses 140 feet of fencing to enclose a rectangular field. If [#permalink] New post   03 Dec 2020, 20:22
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
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Re: A farmer uses 140 feet of fencing to enclose a rectangular field. If [#permalink] New post   06 Dec 2020, 09:15
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Bunuel wrote:
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

Solution:

We see that the length and width of the rectangular field must be 30 and 40 ft, respectively, since 30(2) + 40(2) = 60 + 80 = 140 ft, the fencing (or perimeter) of the field. Therefore, the diagonal must be 50 ft since the length, width and the diagonal of the field form a 3-4-5 right triangle.

Answer: B
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Re: A farmer uses 140 feet of fencing to enclose a rectangular field. If [#permalink]
06 Dec 2020, 09:15
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