CBSE Class 7 Answered
Square and rectangle area is equal and perimeter of rectangle is 40 what will its areas
Asked by Sonimanishkumar94 | 29 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 = .............................(5)
By subtracting eqn.(4) from eqn.(1), and dividing by 2, we get b = .........................(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 . 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 | 29 Jan, 2019, 02:02: PM
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