a)
To find: the sum of areas of four smaller rectangles.
a)
Answer to Problem 28WE
The sum of areas of four smaller rectangles is
Explanation of Solution
Given information:
The given figure is shown below.
Formula used:
Area of a rectangle with length x and breadth y
Calculation:
Consider the given figure.
There are four small rectangles with length a and breadth c , length b and breadth c , length a and breadth d , and length b and breadth d .
Calculate area of the rectangle with length a , and breadth c .
Calculate area of the rectangle with length a , and breadth d .
Calculate area of the rectangle with length b , and breadth c .
Calculate area of the rectangle with length b , and breadth d .
Calculate sum of the areas of small rectangles as shown:
b)
To find: the product of length and breadth of original rectangle.
b)
Answer to Problem 28WE
The product of length and breadth of original rectangle is
Explanation of Solution
Given information:
The given figure is shown below.
Formula used:
Area of a rectangle with length x and breadth y
Calculation:
Consider the given figure.
There are four small rectangles with length a and breadth c , length b and breadth c , length a and breadth d , and length b and breadth d .
Length of the original rectangle is
Breadth of the original rectangle is
Calculate the product of length and breadth of original rectangle as shown:
c)
To explain: the similarity in the answer of part (a) and part (b).
c)
Answer to Problem 28WE
The answer of part (a) and part (b) is same.
Explanation of Solution
Given information:
The given figure is shown below.
Formula used:
Area of a rectangle with length x and breadth y
Calculation:
Consider the given figure.
There are four small rectangles with length a and breadth c , length b and breadth c , length a and breadth d , and length b and breadth d .
Length of the original rectangle is
Breadth of the original rectangle is
Calculate the product of length and breadth of original rectangle as shown:
Calculate sum of the areas of small rectangles as shown:
Area is same in both cases.
Therefore, area of original rectangle is equal to the sum of areas of small rectangles.
Chapter 4 Solutions
Algebra: Structure And Method, Book 1
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