The length of a rectangle is greater than the breadth by 18 cm. If both length and breadth are increased
by 6 cm, then area increases by 168 cm2
. Find the length and breadth of the rectangle.
Answers
Initially assume breadth =x,then length = (x+18)
Area of rectangle = length * breadth
Area = x(x+18)=x^2+18x
Area after increasing length and breadth by 6 cm was (x+6)*(x+24)
New area = x^2+30x+144 ,which is equal to previous area increased by 168
Therefore final equation was
x^2+18x+168= x^2+30x+144
Solving x=2cm ( ie.., breadth of rectangle)
And length = 2+18= 20 cm
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The length of the rectangular plot is 60 % more than its breadth. If the difference between the length and the breadth of that rectangle is 24 cm, what is the area of that rectangle?
The length of a rectangle is 6 cm more than its width. Its length and breadth each is decreased by 36 sq m. What is the original length and breadth of the rectangle?
Area of a rectangle = Length x breath
Breadth = b cm
Length = (b+ 18) cm ( according to the condition of the problem)
Let the Area be ‘ A' cm^2
(b+18)(b) = A
b^2+ 18b = A (1)
New length = b+ 18+6 =( b+24)cm
New breadth = b + 6 cm
New area =( A+ 168) cm^2
(b+24)(b+6) = A+168.
b^2+ 30b + 144 = A+168 (2)
Subtraction eq(1) - eq(2)
12 b +144 = 168 (b^2 & A cancelled)
12b = 168–144
12b = 24
b = 2cm
Breadth = 2cm.
Length = 18+ 2= 20 cm
Verification LB = 20x2= 40 cm^2
(18+6)(6+2) = 24 x 8 = 208 cm^2
So the new area is increased by 168 cm^2 (verified)
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