To find:thelengths of the sides of the
Answer to Problem 4P
The length of sides of small isosceles triangle are 5 cm, 9 cm, and 9 cm. also the length of sides of big isosceles triangle are 5 cm, 18 cm, and 18 cm.
Explanation of Solution
Given information:
Two isosceles triangles have a same base length and the legs of the one of the triangles are twice as long as the legs of the other.
The perimeters of the triangles are 23 cm and 41 cm.
Calculation:
Let x be the lengths of the base in two isosceles triangles.
Let y be the lengths of the legs in small triangle.
The perimeter of the small triangle is 23 cm, so it can be written as the linear equation.
Since the length of legs of big triangle is twice as long as the legs of the small, the length of the leg of the big triangle is 2y .
The perimeter of the big triangle is 21 cm, so it can be written as the linear equation.
Compute the solutions of the system
Subtract the equation
Divide on both sides by2,
Substitute
Thus, the length of sides of small isosceles triangle are 5 cm, 9 cm, and 9 cm.
The length of the legs of the big triangle is
Therefore, the length of sides of big isosceles triangle are 5 cm, 18 cm, and 18 cm.
Chapter 3 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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