To find: the perimeter of the rectangle if there is no space between the cards and no overlap.
Answer to Problem 56E
The perimeter of this rectangle is
Explanation of Solution
Given:
There are nine cards and the area of the rectangle formed by the nine cards is
Concept used:
Perimeter of any shape which has side is the sum of all side.
This problem can be solved using elimination and substitution method.
In the elimination method or substitution method:
Either add or subtract equation to get an equation in one variable.
When the coefficients in one variable are opposites then add the equations to eliminate the variable and when the coefficients of one variable are equal and subtract the equation to eliminate a variable.
Calculation:
Let the length and breadth of a playing card be
There are nine cards and the area of the rectangle formed by the nine cards is
Therefore, it has:
From figure, the length of one side of the rectangle is given by
The length of other side of the rectangle is given by:
By putting
Now from the given figure, the perimeter of the rectangle is:
Hence, the perimeter of this rectangle is
Chapter 3 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
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