Concept explainers
(a)
To represent: The lengths of the sides of the
(a)
Answer to Problem 6P
The variables representing the lengths of the isosceles triangle are a and b.
Explanation of Solution
Given information: An isosceles triangle has perimeter 15 m.
Calculation:
It is given that the triangle is isosceles. Therefore, the triangle has two sides equal. Since the perimeter is the sum of all the sides of the triangle, the perimeter is equal to the sum of two sides having equal length and the third side.
Assume that the length of sides which have equal lengths are a and the length of the third side is b.
Hence, the variables representing the lengths of the isosceles triangle are a and b.
(b)
To write: An open sentence relating to the variables.
(b)
Answer to Problem 6P
The open sentence is
Explanation of Solution
Given information: An isosceles triangle has perimeter 15 m. The variables representing the lengths of the isosceles triangle are a and b.
Calculation:
The perimeter of the isosceles triangle is 15m. That is,
- Here, a is the length of the two sides of the triangle which have equal length and b is the length of the third side.
(b)
To write: An open sentence relating to the variables.
(b)
Answer to Problem 6P
The open sentence is
Explanation of Solution
Given information: An isosceles triangle has perimeter 15 m. The variables representing the lengths of the isosceles triangle are a and b.
Calculation:
The perimeter of the isosceles triangle is 15m. That is,
- Here, a is the length of the two sides of the triangle which have equal length and b is the length of the third side.
(c)
To solve: The open system for integral values.
(c)
Answer to Problem 6P
The only possible integral pairs are
Explanation of Solution
Given information:The open sentence is
Calculation:
The open sentence is
The variable b in terms of a is,
Choose
Choose
Choose
Choose
Choose
Choose
Choose
Choose
This is not possible as b represents the length and length cannot be negative.
Therefore, the only possible integral pairs are,
(c)
To solve: The open system for integral values.
(c)
Answer to Problem 6P
The only possible integral pairs are
Explanation of Solution
Given information:The open sentence is
Calculation:
The open sentence is
The variable b in terms of a is,
Choose
Choose
Choose
Choose
Choose
Choose
Choose
Choose
This is not possible as b represents the length and length cannot be negative.
Therefore, the only possible integral pairs are,
Chapter 3 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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