The areas of a rectangle and a square are in the ratio 3:2. if the length of the rectangle is doubled and the side of the square is tripled find the ratio of their new areas
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Here is your solution
We know that Area of rectangle = length * breadth
We know that Area of square = a^2.
Now,
Given that ratio of area of rectangle and area of square is 3:2.
= > (lb)/(a^2) = 3/2. ------ (1)
(i)
Given that length of rectangle is doubled = 2l.
Area = (2l)(b) = 2lb.
(ii)
Given that Side of square is tripled = 3a.
Area of square = (3a)^2 = 9a^2.
Now,
Ratio of areas:
= > (2lb)/9a^2
= > (2/9) * (lb/a^2)
= > (2/9) * (3/2) {From (i)}
= > 1/3
= > 1 : 3
We know that Area of rectangle = length * breadth
We know that Area of square = a^2.
Now,
Given that ratio of area of rectangle and area of square is 3:2.
= > (lb)/(a^2) = 3/2. ------ (1)
(i)
Given that length of rectangle is doubled = 2l.
Area = (2l)(b) = 2lb.
(ii)
Given that Side of square is tripled = 3a.
Area of square = (3a)^2 = 9a^2.
Now,
Ratio of areas:
= > (2lb)/9a^2
= > (2/9) * (lb/a^2)
= > (2/9) * (3/2) {From (i)}
= > 1/3
= > 1 : 3
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