A rectangle is three times as long as it is high. The area of a square is twelve times the area of the rectangle. What is the ratio of the perimeter of the square to the perimeter of the rectangle?
Give your ratio in its simplest form.
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Answer: 3 : 1
Step-by-step explanation:
Area of square = 12( area of rectangle)
Area of square = l^2 where l is length
Area of rectangle = lb, where b is breadth
l = 3b
A of rectangle = lb = 3b^2
A of square = 12(3b^2) = 36b^2
l of square = sq. root (36b^2)
= 6b
P of rectangle = 2(l + b)
= 2(3b + b)
=8b
P of square = 4l
= 4 x 6b
= 24b
Ratio = 24 : 8
= 3 : 1
Note l for square is not equal to l for rectangle.
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