The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:

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This question was previously asked in

SSC CGL Tier 2 Quant Previous Paper 1 (Held On: 15 November 2020)

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Answer 1

Given:

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