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# In the figure above, x = y. What is the ratio area of (triangle ABC)/

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Math Expert
Joined: 02 Sep 2009
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In the figure above, x = y. What is the ratio area of (triangle ABC)/ [#permalink]

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01 Feb 2018, 00:07
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Difficulty:

15% (low)

Question Stats:

87% (00:49) correct 13% (01:37) wrong based on 55 sessions

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In the figure above, x = y. What is the ratio area of (triangle ABC)/(triangle ADC) ?

(A) 1/2*(x + y)

(B) x + y

(C) xy

(D) 1/2

(E) 1

Attachment:

2018-02-01_1104.png [ 14.24 KiB | Viewed 768 times ]

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In the figure above, x = y. What is the ratio area of (triangle ABC)/ [#permalink]

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01 Feb 2018, 02:48
Bunuel wrote:

In the figure above, x = y. What is the ratio area of (triangle ABC)/(triangle ADC) ?

(A) 1/2*(x + y)

(B) x + y

(C) xy

(D) 1/2

(E) 1

Attachment:
2018-02-01_1104.png

Area of triangle ADC = $$\frac{1}{2}*AD*x$$

Area of triangle ABC = Area of triangle ADB - Area of triangle ADC
Area of triangle ABC = $$\frac{1}{2}*AD*(x+y) - \frac{1}{2}*AD*x = \frac{1}{2}*AD*(2x-x)$$ (as x=y) = Area of triangle ADC

Therefore, Ratio of area of (triangle ABC)/area of (triangle ADC) = 1(Option E)
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Re: In the figure above, x = y. What is the ratio area of (triangle ABC)/ [#permalink]

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01 Feb 2018, 04:17
Bunuel wrote:

In the figure above, x = y. What is the ratio area of (triangle ABC)/(triangle ADC) ?

(A) 1/2*(x + y)

(B) x + y

(C) xy

(D) 1/2

(E) 1

Attachment:
2018-02-01_1104.png

Area of the triangle = (1/2)*Base*Height

For triangle ABC, Area of the triangle = (1/2)*y*AD

But since, x=y hence

Now since Area of ABC/Area of ADC = y/y = 1

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Re: In the figure above, x = y. What is the ratio area of (triangle ABC)/ [#permalink]

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01 Feb 2018, 05:38
Bunuel wrote:

In the figure above, x = y. What is the ratio area of (triangle ABC)/(triangle ADC) ?

(A) 1/2*(x + y)

(B) x + y

(C) xy

(D) 1/2

(E) 1

Altitude of Triangle ABC is AH so area of triangle ABC is 1/2 x Y x AH and Area of Triangle ADC is 1/2 x X x AH. Now the ratio of 2 triangle will cancel everything out so answer is E

Attachment:
2018-02-01_1104.png
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Joined: 22 May 2016
Posts: 1755
In the figure above, x = y. What is the ratio area of (triangle ABC)/ [#permalink]

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01 Feb 2018, 10:27
Bunuel wrote:

In the figure above, x = y. What is the ratio area of (triangle ABC)/(triangle ADC) ?

(A) 1/2*(x + y)

(B) x + y

(C) xy

(D) 1/2

(E) 1

Attachment:
2018-02-01_1104.png

To avoid having to keep track of side names, make a 3-4-5 right triangle, so that AD = 3, BD = 4, and AB = 5

x = y. BD = 4. So x = 2, y = 2

Area of ∆ ABC = $$\frac{b*h}{2}=\frac{2*3}{2}=3$$

Area of ∆ ADC: $$\frac{2*3}{2}=3$$

Ratio of areas?
$$\frac{3}{3}=1$$

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Re: In the figure above, x = y. What is the ratio area of (triangle ABC)/ [#permalink]

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02 Feb 2018, 12:16
Bunuel wrote:

In the figure above, x = y. What is the ratio area of (triangle ABC)/(triangle ADC) ?

(A) 1/2*(x + y)

(B) x + y

(C) xy

(D) 1/2

(E) 1

Attachment:
2018-02-01_1104.png

Since x = y, we see that the base of triangle ABC is equal to that of triangle ADC. We also see that the height of triangle ABC is equal to that of triangle ADC.

Thus, the ratio area of (triangle ABC)/(triangle ADC) = 1.

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Re: In the figure above, x = y. What is the ratio area of (triangle ABC)/   [#permalink] 02 Feb 2018, 12:16
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