Area of a Triangle Find the area of the triangle that lies in the first quadrant (with its base on the x-axis) and that is bounded by the lines y = 2x − 4 and y = −4x + 20.
To find: The area of a triangle that lies in the first quadrant.
Answer to Problem 74E
The area of the triangle is 6 square units.
Explanation of Solution
Given:
The given equation of lines,
Calculation:
Substitute
Substitute 4 for x in equation (1).
Variable y is the height of triangle. The height of triangle is 4.
The distance between x – intercept of both lines is the base of the triangle.
Substitute 0 for y in equation (1) for x-coordinate.
Substitute 0 for y in equation (2) for x-coordinate.
Subtract both x-intercepts to find the base of triangle.
The base of triangle is 3.
Formula to calculate area of triangle is,
Substitute 2 for base and 4 for height in the above formula.
Thus, the area of the triangle is 6 square units.
Chapter 10 Solutions
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