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# A rectangular yard contains two flower beds in the shape of congruent

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
A rectangular yard contains two flower beds in the shape of congruent  [#permalink]

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28 Mar 2019, 06:13
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Difficulty:

25% (medium)

Question Stats:

84% (01:50) correct 16% (02:35) wrong based on 19 sessions

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A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths 15 and 25 meters. What fraction of the yard is occupied by the flower beds?

(A) 1/8
(B) 1/6
(C) 1/5
(D) 1/4
(E) 1/3

Attachment:

3ee29f78e4a8eecdb8faec4092f2f1c361a869e4.png [ 1.33 KiB | Viewed 319 times ]

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A rectangular yard contains two flower beds in the shape of congruent  [#permalink]

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28 Mar 2019, 06:44
Bunuel wrote:

A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths 15 and 25 meters. What fraction of the yard is occupied by the flower beds?

(A) 1/8
(B) 1/6
(C) 1/5
(D) 1/4
(E) 1/3

Attachment:
3ee29f78e4a8eecdb8faec4092f2f1c361a869e4.png

Length of longer side = 25

Length of shorter side = 15

Difference = 25 - 15 = 10

Side of one triangle = 10/2 = 5 units

As the triangle is isosceles, both sides = 5 units each

Area of both triangles = 2 * (1/2*5*5) = 25 units

Total are of rectangular park = 25 * 5 = 125

Required ration = 25 / 125

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A rectangular yard contains two flower beds in the shape of congruent   [#permalink] 28 Mar 2019, 06:44
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