The area of A's rectangle is 8sq cm.The area of Toms rectangle is 5 sq cm.Both rectangles have the same perimeter of 12.Find both length and breadth.
Answers
Step-by-step explanation:
in case 1 - A's rectangle area = 8
so primetre = 2l+2b = 12 (. let b=l)
= 2l= 12
= 2l =12
= l= 12/2 =6
so breadth =2
Answer:
The length and breadth of the rectangle A are either 4 cm & 2 cm or 2 cm & 4 cm respectively.
The length and breadth of Tom's rectangle are either 5 cm & 1 cm or 1 cm & 5 cm respectively.
Step-by-step-explanation:
We have given that,
Area of A's rectangle = 8 sq.cm
Area of Tom's rectangle = 5 sq.cm
Perimeter of both rectangles = 12 cm
We have to find the length and breadth of both of the rectangles.
Let the length of the rectangle A be "x" and breadth be "y" .
And for rectangle of Tom, length be "m" and breadth be "n" .
Now, we know that,
Area of rectangle A = Length * Breadth
⇒ A = xy
⇒ 8 = xy
⇒ x = 8 / y - - - ( 1 )
Now,
Perimeter of rectangle = 2 ( Length + Breadth )
⇒ P = 2 ( x + y )
⇒ 12 = 2 ( x + y )
⇒ x + y = 12 ÷ 2
⇒ x + y = 6
⇒ 8 / y + y = 6 - - - [ From ( 1 ) ]
⇒ 8 + y² / y = 6
⇒ 8 + y² = 6y
⇒ y² - 6y + 8 = 0
⇒ y² - 4y - 2y + 8 = 0
⇒ y ( y - 4 ) - 2 ( y - 4 ) = 0
⇒ ( y - 4 ) ( y - 2 ) = 0
⇒ y - 4 = 0 OR y - 2 = 0
⇒ y = 4 OR y = 2
By substituting y = 4 in equation ( 1 ), we get,
x = 8 / y - - - ( 1 )
⇒ x = 8 / 4
⇒ x = 2
Now, by substituting y = 2 in equation ( 1 ), we get,
x = 8 / y - - - ( 1 )
⇒ x = 8 / 2
⇒ x = 4
∴ The length and breadth of the rectangle A are either 4 cm & 2 cm or 2 cm & 4 cm respectively.
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For Tom's rectangle,
Area = Length * Breadth
⇒ A = mn
⇒ 5 = mn
⇒ m = 5 / n - - - ( 2 )
Now,
Perimeter of rectangle = 2 ( Length + Breadth )
⇒ P = 2 ( m + n )
⇒ 12 = 2 ( m + n )
⇒ m + n = 12 ÷ 2
⇒ m + n = 6
⇒ 5 / n + n = 6 - - - [ From ( 2 ) ]
⇒ 5 + n² / n = 6
⇒ 5 + n² = 6n
⇒ n² - 6n + 5 = 0
⇒ n² - 5n - n + 5 = 0
⇒ n ( n - 5 ) - 1 ( n - 5 ) = 0
⇒ ( n - 5 ) ( n - 1 ) = 0
⇒ n - 5 = 0 OR n - 1 = 0
⇒ n = 5 OR n = 1
By substituting n = 5 in equation ( 2 ), we get,
m = 5 / n - - - ( 2 )
⇒ m = 5 / 5
⇒ m = 1
Now, by substituting n = 1 in equation ( 2 ), we get,
m = 5 / n - - - ( 2 )
⇒ m = 5 / 1
⇒ m = 5
∴ The length and breadth of Tom's rectangle are either 5 cm & 1 cm or 1 cm & 5 cm respectively.