# Thread: ratio of the area of square and rectangle

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## ratio of the area of square and rectangle

The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2:3, what is the ratio of the area of region R to area of region S ?

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Ratio of the sides of R =2:3=2x and 3x [suppose]
Perimeter of R=Perimeter of S=10x
Area of R=6x^2
Area of S=(10x/4)^2=(100x^2)/16

Area of R/Area of S=(6x^2)*16/100x^2=24:25

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4. Good post? |
Can any one please provide elaborate explanation on CTG1983's explanation for this question... please... I did not understand even a bit....

Thank You....

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Originally Posted by asur
Can any one please provide elaborate explanation on CTG1983's explanation for this question... please... I did not understand even a bit....

Thank You....
Perimeter of square = Perimeter of rectangle
4a = 2l+2w

Since the sides of rectangle are 2:3, lets plug the values to the above equation

4a = 2*2+2*3
a= 5/2

So the side of the square is 5/2

Area of rectangle/Area of square = (2*3)/(5/2)^2 = 24/25

6. Good post? |
let "a" be the side of the square S,"w" and "l" be the sides of the recatangle R. According to the questions,

Perimeter of square = perimeter of rectangle.
4a = 2w + 2l

Now, w/l = 2/3

therefore,

4a = 2w+2*(3w/2)
4a = 5w and l = 6/5a

Area of rectangle. = w*l = 4/5a * 6/5a =24/25*a^2
Area of squage = a ^2

Take the ratio; you will get 24/25

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Thank you for posting it... I got it now!