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What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12

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What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12 [#permalink] What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12   05 Aug 2020, 11:42
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What is the area of the triangle formed by lines \(4x+5y=20\), \(3y-4x=12\), and the \(x-\)axis?

A) 10
B) 12
C) 16
D) 20
E) 30
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C
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Re: What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12 [#permalink] What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12   05 Aug 2020, 12:37
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The x-intercept and y-intercept of \(4x+5y=20\) are 5 and 4 respectively

The x-intercept and y-intercept of \(3y-4x=12\) are -3 and 4 respectively

Area of the triangle \(= \frac{1}{2} * 4*(5-(-3)) = 16\)


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What is the area of the triangle formed by lines \(4x+5y=20\), \(3y-4x=12\), and the \(x-\)axis?
A) 10
B) 12
C) 16
D) 20
E) 30
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What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12 [#permalink] What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12   07 Aug 2020, 02:22
TheUltimateWinner
What is the area of the triangle formed by lines \(4x+5y=20\), \(3y-4x=12\), and the \(x-\)axis?

A) 10
B) 12
C) 16
D) 20
E) 30

Thank you for the question. Took me actually longer than expected; totally forgot about linear equations.
Visualising it helped me a lot. See picture attached. By plugging in X=0 and Y=0 in both equations you get two lines. Then you calculate both areas and add them up.

Final answer = C, so 16
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Re: What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12 [#permalink] What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12   07 Aug 2020, 02:51
Expert Reply
Given
    • Three lines,
      o 4x+5y=20
      o 3y−4x=12
      o x−axis
To Find

    • Area of the triangle formed by these lines.

Approach and Working Out

    • 4x+5y=20
      o \(\frac{x}{5}\) + \(\frac{y}{4}\) = 1
    • 3y−4x=12
      o \(\frac{y}{4}\) – \(\frac{x}{3}\) = 1
    • y = 0

    • Area of the triangle formed = ½ × height × base

      =\(\frac{1}{2}\) × 4 × 8
      = 16
Correct Answer: Option C
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Re: What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12 [#permalink] What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12   15 Sep 2021, 07:43
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Re: What is the area of the triangle formed by lines 4x + 5y =20, 3y-4x=12 [#permalink]
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