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

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Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139442 [0], given: 12790

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

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10 Oct 2017, 23:47
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Difficulty:

25% (medium)

Question Stats:

88% (01:30) correct 13% (01:58) wrong based on 48 sessions

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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

_________________

Kudos [?]: 139442 [0], given: 12790

Senior Manager
Joined: 05 Dec 2016
Posts: 260

Kudos [?]: 27 [0], given: 49

Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: The width of a rectangular playground is 75 percent of its length. If [#permalink]

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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

Kudos [?]: 27 [0], given: 49

VP
Joined: 22 May 2016
Posts: 1249

Kudos [?]: 458 [0], given: 682

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

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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*

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

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Kudos [?]: 458 [0], given: 682

Intern
Joined: 10 Apr 2017
Posts: 37

Kudos [?]: 8 [0], given: 194

Schools: Kelley '20
Re: The width of a rectangular playground is 75 percent of its length. If [#permalink]

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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

Kudos [?]: 8 [0], given: 194

Intern
Joined: 24 Oct 2016
Posts: 25

Kudos [?]: 0 [0], given: 16

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

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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.

Kudos [?]: 0 [0], given: 16

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