Question
Download Solution PDFWhat is the area (in square units) of the triangle formed by the graphs of the equations: 2x - y + 8 = 0 and 8x + 3y - 24 = 0, and y = 0?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Equations of the lines: 2x - y + 8 = 0, 8x + 3y - 24 = 0, and y = 0
Formula used:
Area of triangle formed by lines = 1/2 × base × height
Calculation:
Solve for intersection points:
Line 1: 2x - y + 8 = 0
⇒ y = 2x + 8
Line 2: 8x + 3y - 24 = 0
Substitute y from Line 1 into Line 2:
8x + 3(2x + 8) - 24 = 0
⇒ 8x + 6x + 24 - 24 = 0
⇒ 14x = 0
⇒ x = 0
Substitute x = 0 into Line 1:
y = 2(0) + 8 = 8
Intersection points are: (0, 8) and y = 0 intersects these lines at x-values:
For 2x - y + 8 = 0, y = 0:
2x + 8 = 0
⇒ x = -4
For 8x + 3y - 24 = 0, y = 0:
8x - 24 = 0
⇒ x = 3
Base = Distance between (-4, 0) and (3, 0) = 7 units
Height = 8 units
Area = 1/2 × base × height
⇒ Area = 1/2 × 7 × 8
⇒ Area = 28 sq units
∴ The correct answer is option (1).
Last updated on Dec 9, 2024
-> SSC Head Constable (AWO/TPO) 2025 Notification will be announced soon.
-> SSC Head Constable (AWO/TPO) Marks were out for the previous cycle. Candidates could check their marks from the official website till 15th February 2024.
-> The total number of vacancies for the SSC Head Constable 2025 Notification will be declared soon. The candidates earlier appeared for the exam for a total number of 857 vacancies for SSC Head Constable Recruitment for the 2022 cycle.
->The candidates who will be qualified in the CBE gets eligible for the Physical test. Candidates can improve their preparations and score high by referring to SSC Head Constable AWO TPO Previous Years Papers and SSC Head Constable (AWO/TPO) Mock Test.