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Thread: ratio of the area of square and rectangle

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    ratio of the area of square and rectangle

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    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 ?

    Answer 24 : 25

    please explain??
    Last edited by kamranalam81; 01-03-2006 at 04:59 AM.

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    TestMagic Guru CTG1983's Avatar
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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

    por favor, el seņor check thy answer again.

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    Thanx... your answer is correct





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    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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    Quote 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

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    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!

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