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5. Find the area of the triangular region defined by the system of inequalities shown below

y>x x>-3 y<6

1 Answer

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Answer:

40.5 square units

Explanation:

x > -3 → dashed line at x = 3

→ shading to the right of the line x = 3

y < 6 → dashed line at y = 6

→ shading under the line y = 6

y > x → dashed line at y = x

→ shading above the line y = x

Therefore, we have:

  • horizontal line: x = -3
  • vertical line: y = 6
  • diagonal line: y = x

The vertices of the triangle formed are where the lines intersect with eachother.

As we have a horizontal and vertical line, the point at which they meet is a right angle vertex → (-3, 6)

To find the other two points:

  • y = x meets x = -3 at (-3, -3)
  • y = x meets y = 6 at (6, 6)

The height of the triangle is the y-value of (-3, 6) less the y-value of (-3, -3):

⇒ height = 6 - (-3) = 9

The base (width) of the triangle is the x-value of (6, 6) less the x-value of (-3, 6):

⇒ base =6 - (-3) = 9

Area of a triangle = 1/2 × base × height

= 1/2 × 9 × 9

= 40.5 square units

5. Find the area of the triangular region defined by the system of inequalities shown-example-1
User J  Calbreath
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