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In the rectangle above, what is the ratio of (area of shaded region)

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In the rectangle above, what is the ratio of (area of shaded region) [#permalink]

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New post 05 Feb 2018, 06:53
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A
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In the rectangle above, what is the ratio of (area of shaded region)/(area of unshaded region)

(A) 1:4
(B) 1:2
(C) 1:1
(D) 2:1
(E) 3:1

Attachment:
2018-02-05_1750.png
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In the rectangle above, what is the ratio of (area of shaded region) [#permalink]

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In the rectangle above, the triangle with similar base and height will have an equal area.
Hence, Area(Triangle 1) = Area(Triangle 2)
Similarly, Area(Triangle 3) = Area(Triangle 4)

Area(Triangle2) + Area(Triangle3) = Area(Triangle1) + Area(Triangle4)

Therefore, (area of shaded region) = (area of unshaded region)

The ratio of (area of shaded region)/(area of unshaded region) is 1:1(Option C)
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Re: In the rectangle above, what is the ratio of (area of shaded region) [#permalink]

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New post 05 Feb 2018, 07:54
Area of unshaded = 1/2 * x * y

Area of shaded = 1/2 * x * a + 1/2 * x * (y - a) = 1/2 * x * y

Ratio of shaded to unshaded = 1 : 1

Answer: C
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Re: In the rectangle above, what is the ratio of (area of shaded region) [#permalink]

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New post 06 Feb 2018, 18:02
Bunuel wrote:
Image
In the rectangle above, what is the ratio of (area of shaded region)/(area of unshaded region)

(A) 1:4
(B) 1:2
(C) 1:1
(D) 2:1
(E) 3:1

Attachment:
2018-02-05_1750.png


We can let the base of the unshaded triangle = the length of rectangle = n.

We can let the height of the unshaded triangle = width of the rectangle = h.

The area of the unshaded region is the area of the unshaded triangle, which is:

1/2 x n x h = nh/2

The area of the shaded region is the difference between the area of the rectangle and the area of the unshaded triangle:

nh - nh/2 = 2nh/2 - nh/2 = nh/2

So the ratio is 1 : 1.

Answer: C
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Re: In the rectangle above, what is the ratio of (area of shaded region) [#permalink]

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New post 07 Feb 2018, 02:17
Bunuel wrote:
Image
In the rectangle above, what is the ratio of (area of shaded region)/(area of unshaded region)

(A) 1:4
(B) 1:2
(C) 1:1
(D) 2:1
(E) 3:1

Attachment:
2018-02-05_1750.png


Area of Unshaded region = \(\frac{1}{2}*l*b\)
Area of Rectangle = \(l*b\)
\(Ratio = (\frac{Total Area}{Area of Unshaded Region}) - 1\) = 1
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Re: In the rectangle above, what is the ratio of (area of shaded region)   [#permalink] 07 Feb 2018, 02:17
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