In rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.
The area of a rectangle is the product of its length and its width.
In the question, we are given two rectangles:-
Rectangle P:
length = 40 cm,
width = x cm,
Thus, the area = length * width = 40x.
Rectangle Q:
length = 25% more than the length of P = 40 + 25% of 40 = 40 + 0.25*40 = 40 + 10 = 50 cm.
width = y cm,
Thus, the area = length * width = 50y.
Now, we are given that, the area of rectangle Q is 10% less than the area of rectangle P.
Thus, we can write that,
Area of rectangle Q = Area of rectangle P - 10% of the area of rectangle P,
or, 50y = 40x - 10% of 40x,
or, 50y = 40x - 0.10*40x,
or, 50y = 40x - 4x,
or, 50y = 36x,
or, y = 36x/50.
We are asked to find the ratio of x:y = x/y.
Substituting y = 36x/50, we get,
x/y = x/(36x/50) = 50x/36x = 25/18.
Thus, the ratio x:y = 25:18.
Thus, in rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.
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