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a)
To find: the sum of areas of four smaller rectangles.
a)
![Check Mark](/static/check-mark.png)
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)
![Check Mark](/static/check-mark.png)
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)
![Check Mark](/static/check-mark.png)
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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