Answer The area of the triangle is 24 . Explanation Given: The given equations are, 2 x + y = 5 y = x − 4 y = 5 Calculation: Consider the given equations is, 2 x + y = 5 y = x − 4 y = 5 The graph for the equations is shown in Figure 1 Figure 1 The intersection points of the line is at x = 0 and x = 9 . Thus, the base of the triangle is 9 . The intersections of the y axis is at y = − 1 .Then the height of the triangle is, 5 − ( − 1 ) = 6 . Thus, the area of the triangle is, 1 2 ( 8 ) ( 6 ) = 24

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 9.1, Problem 24WE

To determine

To find: The area of the region whose vertices are the point of the intersection of the given equations.

Expert Solution & Answer

Answer to Problem 24WE

The area of the triangle is 24 .

Explanation of Solution

Given:

The given equations are,

2x+y=5y=x−4y=5

Calculation:

Consider the given equations is,

2x+y=5y=x−4y=5

The graph for the equations is shown in Figure 1

Algebra: Structure And Method, Book 1, Chapter 9.1, Problem 24WE

Figure 1

The intersection points of the line is at x=0 and x=9 . Thus, the base of the triangle is 9 .

The intersections of the y axis is at y=−1 .Then the height of the triangle is,

5−(−1)=6 .

Thus, the area of the triangle is,

12(8)(6)=24

Chapter 9.1, Problem 23WE

Chapter 9.1, Problem 1MRE

Chapter 9 Solutions

Algebra: Structure And Method, Book 1

Ch. 9.1 - Prob. 1OE Ch. 9.1 - Prob. 2OE Ch. 9.1 - Prob. 3OE Ch. 9.1 - Prob. 4OE Ch. 9.1 - Prob. 5OE Ch. 9.1 - Prob. 6OE Ch. 9.1 - Prob. 7OE Ch. 9.1 - Prob. 8OE Ch. 9.1 - Prob. 9OE Ch. 9.1 - Prob. 1WE

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