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# The figure above represents a triangular field. What is the minimum di

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Math Expert
Joined: 02 Sep 2009
Posts: 60646
The figure above represents a triangular field. What is the minimum di  [#permalink]

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22 Oct 2019, 22:13
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5% (low)

Question Stats:

88% (01:12) correct 12% (01:25) wrong based on 43 sessions

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The figure above represents a triangular field. What is the minimum distance, in meters, that a person would have to walk to go from point A to a point on side BC?

A. 50
B. 60
C. 70
D. 80
E. 90

Attachment:

traingle.jpg [ 5.11 KiB | Viewed 530 times ]

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Joined: 18 Jul 2019
Posts: 25
Re: The figure above represents a triangular field. What is the minimum di  [#permalink]

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14 Nov 2019, 02:31
1
Luca1111111111111 wrote:
The triangle has two sides with equal length. Their opposite angles must therefore also be of opposite length. We can conclude that this is an isosceles triangle.
The shortest way is a straight line from A to the line BC which is the height of the triangle. We call it D. D splits the triangle in two identical triangle, creating a 90° angle. This lets us apply the Pythagoras Theorem a^2 + b^2 = c^2.
In this case this would be a^2 + 80^2 = 100^2. As a result, solving for a, we get a = 60. The answer is B

HI,
How can we say that a perpendicular dropped from the vertex A would divide the triangle symmetrically? I feel like I know this to be true, but would like to pinpoint a proof or rule for this. Thanks.
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Re: The figure above represents a triangular field. What is the minimum di  [#permalink]

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22 Oct 2019, 22:19
Bunuel wrote:

The figure above represents a triangular field. What is the minimum distance, in meters, that a person would have to walk to go from point A to a point on side BC?

A. 50
B. 60
C. 70
D. 80
E. 90

Attachment:
traingle.jpg

drop a perpendicular D from A to side BC ; BC = 80 ; AC= 100 and AD =60
∆ 5:4:3 ;
IMO B ; 60
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Joined: 20 Apr 2019
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Re: The figure above represents a triangular field. What is the minimum di  [#permalink]

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29 Oct 2019, 12:29
The triangle has two sides with equal length. Their opposite angles must therefore also be of opposite length. We can conclude that this is an isosceles triangle.
The shortest way is a straight line from A to the line BC which is the height of the triangle. We call it D. D splits the triangle in two identical triangle, creating a 90° angle. This lets us apply the Pythagoras Theorem a^2 + b^2 = c^2.
In this case this would be a^2 + 80^2 = 100^2. As a result, solving for a, we get a = 60. The answer is B
Re: The figure above represents a triangular field. What is the minimum di   [#permalink] 29 Oct 2019, 12:29
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