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The width of a rectangular playground is 75 percent of its length. If

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The width of a rectangular playground is 75 percent of its length. If [#permalink]

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New post 10 Oct 2017, 23:47
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The width of a rectangular playground is 75 percent of its length. If the perimeter of the playground is 280 meters, how long, in meters, is a straight path that cuts diagonally across the playground from one corner to another?

(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
[Reveal] Spoiler: OA

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Re: The width of a rectangular playground is 75 percent of its length. If [#permalink]

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New post 11 Oct 2017, 00:14
length = x
width = 3/4x
P=280=2*(x+3/4x)
solving
x=80

Using pythagorean formula we find that diagonal = 100

Answer E.

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The width of a rectangular playground is 75 percent of its length. If [#permalink]

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New post 11 Oct 2017, 05:40
Bunuel wrote:
The width of a rectangular playground is 75 percent of its length. If the perimeter of the playground is 280 meters, how long, in meters, is a straight path that cuts diagonally across the playground from one corner to another?

(A) 60
(B) 70
(C) 80
(D) 90
(E) 100

Perimeter = 2W + 2L

W = \(\frac{3}{4}\)L

P = 2\((\frac{3}{4})\)L + 2L

280 = \(\frac{3}{2}\)L + 2L
560 = 7L
L = 80
W = 60

The diagonal is the hypotenuse of a right triangle. This is a 3: 4: 5 right triangle.

Its legs of 60 and 80 correspond with ratio of 3 to 4. Multiplier = 20. So 60: 80: 100 = length of diagonal*

Answer E

*Or:
\(60^2 + 80^2 = d^2\)
\(3600 + 6400 = d^2\)
\(10,000 = d^2\)
\(d = 100\)

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Re: The width of a rectangular playground is 75 percent of its length. If [#permalink]

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New post 14 Oct 2017, 09:27
The width of a rectangular playground is 75 percent of length"
W = 0.75L

"the perimeter of the playground is 280 meters"
2W + 2L = 280
W + L = 140
0.75L + L = 140
L = 140/1.75 = 80
W = 60
diagonal = √(L² + W²) = 100 meters

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Re: The width of a rectangular playground is 75 percent of its length. If [#permalink]

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New post 15 Oct 2017, 03:50
W = 0.75L
Perimeter of a rectangle = 2 * (L + W)

So 2 * (L + 0.75L) = 280 ==> L = 80 & W = 0.75 * 80 = 60

The path represents the diagonal of a rectangle that can be found applying the Pythagorean Theorem:

Length of diagonal path = √((80)^2 + (60) ^2) = 100

E.

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Re: The width of a rectangular playground is 75 percent of its length. If   [#permalink] 15 Oct 2017, 03:50
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