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

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

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05 Feb 2018, 05:53
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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

[Reveal] Spoiler:
Attachment:

2018-02-05_1750.png [ 13.04 KiB | Viewed 361 times ]
[Reveal] Spoiler: OA

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

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05 Feb 2018, 06:52
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2018-02-05_1750.png [ 13.9 KiB | Viewed 243 times ]

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)

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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05 Feb 2018, 06:54
Area of unshaded = 1/2 * x * y

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

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

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06 Feb 2018, 17:02
Bunuel wrote:

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

[Reveal] Spoiler:
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.

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

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07 Feb 2018, 01:17
Bunuel wrote:

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

[Reveal] Spoiler:
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, 01:17
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