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Calculate the dimensions of a rectangle whose diagonal is 75m, knowing that is similar to a rectangle with sides measuring 36m*48m respectively?

Let the sides of the rectangle be x and y

diagonal is 75 m.

similar rectangle has two sides 36m. and 48m.

let its diagonal be D

By pythagoras theorem

D2= 362 + 482

D2= 1296 + 2304

D2= 3600

D = 60 m.

So the triangle in first rectangle is similar to triangle in second rectangle

so      x/48 = y/36 = 75/60

          x/48 = 75/60                   y/36 = 75/60

         x = 60 m.                          y = 45m.

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if the I rectangle is similar to the second one, their diagnols must be in some specific ratio.

diagnol of the second rectangle = x

x2= 362+ 482 = 1296 + 2304 = 3600

x = 60 metres.

diagnol of the first rectangle = 75.............(given)

thus, ratio of the diagnols = 60/75 = 4/5........(I)

required lenght = a

required breadth = b

thus ratio of the lenghts and breadth will alsso be the same i.e. 4/5.

lenght of the II rect./ lenght of I rectangle = 4/5

36/a = 4/5

a = 45 metres
 

48/b = 4/5

b= 60 metres.

thus, the required dimmensions are 45 m and 60 m.

nice question......

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