Concept explainers
To calculate: The sum of the perimeters of the square.
Answer to Problem 3P
The sums of perimeter of the squares are
Explanation of Solution
Given information: The side of 1st square is 12 cm
Figure:
According to the question, square 2 is formed by joining the mid-points of square 1, square 3 is formed by joining the mid-points of square 2 and so on.
Perimeter of first square = 4 ×12 = 48 cm
Therefore, side of the second square:
P is midpoint of AB
PB = BQ = 6cm
Apply the Pythagoras Theorem:
Hence, the sides of second square
Therefore, perimeter = 4×
Similarly,
Side of Third Square:
Perimeter = 4×6 = 24 cm
Hence, the perimeters of all square are in GP
Therefore,
The first term,
Second terms,
The common ratio,
Formula used: As we know sum of infinity term of a G.P is
Calculation:
Hence, the sums of perimeter of the squares are
Chapter 11 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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