Square and rectangle area is equal and perimeter of rectangle is 40 what will its areas

Asked by Sonimanishkumar94 | 29th Jan, 2019, 12:19: PM

Expert Answer:

Let l and b are length and breadth of rectangle.
 
perimeter 2(l+b) = 40  or (l+b) = 20 ....................(1)
 
if a is side of square, its area is a2 . since area of rectangle and square are equal, we have,   l × b = a2 ................(2)
 
we have, (l-b)2 = (l+b)2 -4lb ...................(3)
 using eqns.(1) and (2), we get (l-b) in (3) as,  ( l - b ) = 400 - 4a2 ..............................(4)
 
By adding eqns.(1) and (4), and dividing by 2, we get l = begin mathsize 12px style 10 space plus space square root of 100 minus a squared end root end style .............................(5)
By subtracting eqn.(4) from eqn.(1), and dividing by 2, we get b = begin mathsize 12px style 10 space minus space square root of 100 space minus space a squared end root end style  .........................(6)
by substituting values for a, so that a <10 in eqns.(5) and (6), we get the dimensions for rectangle and square of equal area.
 
example if a = 9,  length and breadth of rectangles are respectively begin mathsize 12px style 10 plus square root of 19 space space a n d space 10 minus square root of 19 end style. It can be checked that area square or rectangle is 81
if a = 8,  length and breadth of rectangles are respectively 16 and 4. It can be checked that area square or rectangle is 64

Answered by Thiyagarajan K | 29th Jan, 2019, 02:02: PM

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