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What is the area of the triangle formed by the lines y = 2x − 6, x = 9

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What is the area of the triangle formed by the lines y = 2x − 6, x = 9  [#permalink]

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New post 23 May 2018, 22:47
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:35) correct 33% (01:42) wrong based on 137 sessions

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Re: What is the area of the triangle formed by the lines y = 2x − 6, x = 9  [#permalink]

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New post 24 May 2018, 00:12
1
Bunuel wrote:
What is the area of the triangle formed by the lines y = 2x − 6, x = 9, and y = 0?

A. 21
B. 27
C. 36
D. 48
E. 54


If \(0=2x-6\), then \(x=3\).
So, the base of the triangle is \(9-3=6\).

If \(x=9\), then \(y=2*9-6=12\)
So, the height of the triangle is \(12\).

\(S=0.5*6*12=36\).

Answer: C
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Re: What is the area of the triangle formed by the lines y = 2x − 6, x = 9  [#permalink]

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New post 24 May 2018, 01:14

Solution



Given:
• The equations of the lines forming the triangle are
    o y = 2x – 6
    o x = 9
    o y = 0

To find:
• The area of the triangle formed by the three lines

Approach and Working:
If we solve the three equations by taking two at a time, we can get the vertices as (3, 0), (9, 0), and (9, 12)
• Distance between (3, 0) and (9, 0) = 6 units
• As the x-coordinates of the points (9, 0) and (9, 12) are same, the distance between these two points indicate the height of the triangle
    o Height = 12 units
• Hence, the area of the triangle = ½ * 6 * 12 sq. unit = 36 sq. unit

Hence, the correct answer is option C.

Answer: C
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Re: What is the area of the triangle formed by the lines y = 2x − 6, x = 9  [#permalink]

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New post 22 Jul 2018, 02:22
Tulkin987 wrote:
Bunuel wrote:
What is the area of the triangle formed by the lines y = 2x − 6, x = 9, and y = 0?

A. 21
B. 27
C. 36
D. 48
E. 54


If \(0=2x-6\), then \(x=3\).
So, the base of the triangle is \(9-3=6\).

If \(x=9\), then \(y=2*9-6=12\)
So, the height of the triangle is \(12\).

\(S=0.5*6*12=36\).

Answer: C



Bunuel why when it comes to base we need to make subtraction between two values \(9-3=6\) but when it comes to calculating height we dont do any similar subtraction ? :?
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Re: What is the area of the triangle formed by the lines y = 2x − 6, x = 9  [#permalink]

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New post 30 Jul 2018, 23:33
EgmatQuantExpert wrote:

Solution



Given:
• The equations of the lines forming the triangle are
    o y = 2x – 6
    o x = 9
    o y = 0

To find:
• The area of the triangle formed by the three lines

Approach and Working:
If we solve the three equations by taking two at a time, we can get the vertices as (3, 0), (9, 0), and (9, 12)
• Distance between (3, 0) and (9, 0) = 6 units
• As the x-coordinates of the points (9, 0) and (9, 12) are same, the distance between these two points indicate the height of the triangle
    o Height = 12 units
• Hence, the area of the triangle = ½ * 6 * 12 sq. unit = 36 sq. unit

Hence, the correct answer is option C.

Answer: C


Can you explain this problem in detail?
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Re: What is the area of the triangle formed by the lines y = 2x − 6, x = 9  [#permalink]

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New post 31 Jul 2018, 01:29
1
Seryozha wrote:
EgmatQuantExpert wrote:

Solution



Given:
• The equations of the lines forming the triangle are
    o y = 2x – 6
    o x = 9
    o y = 0

To find:
• The area of the triangle formed by the three lines

Approach and Working:
If we solve the three equations by taking two at a time, we can get the vertices as (3, 0), (9, 0), and (9, 12)
• Distance between (3, 0) and (9, 0) = 6 units
• As the x-coordinates of the points (9, 0) and (9, 12) are same, the distance between these two points indicate the height of the triangle
    o Height = 12 units
• Hence, the area of the triangle = ½ * 6 * 12 sq. unit = 36 sq. unit

Hence, the correct answer is option C.

Answer: C


Can you explain this problem in detail?



hi there Seryozha i myself was stumped by this question but figured it out finally how it is solved :)

we have following data y = 2x − 6, x = 9, and y = 0

1. lets find height of triangle

to do this you plug in x = 9 into y = 2x − 6 so we have y = 2 (9) − 6 = 12

so we know that height is y = 12 , now lets find x; to do this set y=0 ----> 0 = 2x − 6 ---> 2x=6 ---> x =3

so we have now coordinate of one point (12;3) where 12 is height of triangle

now we need to find base as you see we are already given that x = 9 and y = 0 , hence this is a another point (9;0)

to find area of triangle 1/2 *base*height --> 1/2*6*12 = 36

see attached a diagram :)

cheers :-)
Attachments

coordinate_geometry.png
coordinate_geometry.png [ 106.64 KiB | Viewed 493 times ]


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Re: What is the area of the triangle formed by the lines y = 2x − 6, x = 9 &nbs [#permalink] 31 Jul 2018, 01:29
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