Question
Download Solution PDFThe area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
8x + 3y = 24, 2x + 8 = y and the x-axis
Formula used:
Area of triangle = 1/2 × base × height
The Y co-ordinate of point of intersection of the two lines 8x + 3y = 24, 2x + 8 = y gives the height of the triangle.
The difference between the x intercepts of the lines 8x + 3y = 24, 2x + 8 = y gives the base of the triangle
Calculation:
For 8x + 3y = 24, 2x + 8 = y to find the point of intersection put one equation in other
⇒ 8x + 3(2x + 8) = 24
⇒ 14x = 0
⇒ x = 0
⇒ y = 2×0 + 8 = 8
⇒ Height of the triangle = 8
For 8x + 3y = 24, 2x + 8 = y to find the X – intercepts put y = 0
⇒ 8x + 3×0 = 24
⇒ x1 = 3
⇒ 2x + 8 = 0
⇒ x2 = -4
Their difference is the base = 3 – (-4) = 7
∴ The area of triangle = 8 × 7/2 = 28
Last updated on Jul 19, 2025
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