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# In the figure above, (a + b + c)/(s + t + u) =

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Math Expert
Joined: 02 Sep 2009
Posts: 55150
In the figure above, (a + b + c)/(s + t + u) =  [#permalink]

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12 Aug 2017, 03:10
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Difficulty:

35% (medium)

Question Stats:

72% (01:06) correct 28% (00:56) wrong based on 64 sessions

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In the figure above, (a + b + c)/(s + t + u) =

(A) 1/3
(B) 1/2
(C) 2/3
(D) 1
(E) 3/2

Attachment:

2017-08-12_1405.png [ 7.15 KiB | Viewed 758 times ]

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In the figure above, (a + b + c)/(s + t + u) =  [#permalink]

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12 Aug 2017, 03:55
Bunuel wrote:

In the figure above, (a + b + c)/(s + t + u) =

(A) 1/3
(B) 1/2
(C) 2/3
(D) 1
(E) 3/2

Attachment:
2017-08-12_1405.png

Interior angles sum to 180
a + b + c = 180
Exterior angles sum to 360
s + t + u = 360

(a + b + c)/(s + t + u) = 180/380

$$\frac{180}{360}$$ = $$\frac{1}{2}$$

OR (exterior angle = sum of two non-adjacent angles)

b + c = s
a + c = t
a + b = u

b + c + a + c + a + b = s + t + u

2(a + b + c) = (s + t + u)

2(a + b + c)/(s + t + u) = 1

(a + b + c)/(s + t + u) = 1/2

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In the figure above, (a + b + c)/(s + t + u) =  [#permalink]

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12 Aug 2017, 04:02
Bunuel wrote:

In the figure above, (a + b + c)/(s + t + u) =

(A) 1/3
(B) 1/2
(C) 2/3
(D) 1
(E) 3/2

Attachment:
2017-08-12_1405.png

Can be solved Using the properties of exterior angles of triangle.

Exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

$$s = b + c$$
$$t = a + c$$
$$u = a + b$$

$$s + t + u = b + c + a + c + a + b => 2a + 2b + 2c$$

$$s + t + u = 2 (a + b + c)$$

$$\frac{(a + b + c)}{(s + t + u)} = \frac{(a + b + c)}{2(a + b + c)} = \frac{1}{2}$$

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Re: In the figure above, (a + b + c)/(s + t + u) =  [#permalink]

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12 Aug 2017, 04:16
Top Contributor
Bunuel wrote:

In the figure above, (a + b + c)/(s + t + u) =

(A) 1/3
(B) 1/2
(C) 2/3
(D) 1
(E) 3/2

Attachment:
2017-08-12_1405.png

$$\frac{(a + b + c)}{(s + t + u)}$$=$$\frac{180}{(180-a+180-b+180-c)}$$=$$\frac{180}{3*180-(a+b+c)}$$=$$\frac{180}{3*180-180}$$=$$\frac{180}{2*180}$$=$$\frac{1}{2}$$

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Re: In the figure above, (a + b + c)/(s + t + u) =  [#permalink]

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12 Aug 2017, 04:30
1
take any random value for a,b and c say a30, b120, c 30. and sum of a,b,c is 180
accordingly s ,t, u will be 180-30, 180-120, 180- 30 i.e. 150,60 and 150 and thoer sum will be 360
(a+b+c)/ (r+s+t) = 180/360 =1/2 which is option B
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Re: In the figure above, (a + b + c)/(s + t + u) =  [#permalink]

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12 Aug 2017, 08:32
1
In the figure above, (a + b + c)/(s + t + u) =

(A) 1/3
(B) 1/2
(C) 2/3
(D) 1
(E) 3/2

s=b+c
t=c+a
u=b+a
a+b+c =180

therefore, a+b+c / s+t+u = (a+b+c) / 2 (a+b+c) = 1/2
Re: In the figure above, (a + b + c)/(s + t + u) =   [#permalink] 12 Aug 2017, 08:32
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# In the figure above, (a + b + c)/(s + t + u) =

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