the perimeters of two squares are 60cm and 32cm respectively. find the length of the diagonal of the square whose area is equal to the sum of the areas of these two squares.
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Perimeter of the first square = 60 cm
one side of it = 60/4 = 15cm
area of this square = 15*15 = 225
perimeter of the second square = 32cm
one side of this square = 32/4 = 8
area of this square = 8*8 = 64
area of square whose area is equal to the sum of these two = 225 +64 = 289
one side of this square will be underroot of 289 i.e. 17
to caculate the length of the diagonal we consider any one of the triangles made by the diagonal.
using pythagoras theorem, we get
17square +17 square = diagonal square
289+289 = diagonal square
578 = diagonal's square
therefore, diagonal will be underroot of 578
which is
24.09
one side of it = 60/4 = 15cm
area of this square = 15*15 = 225
perimeter of the second square = 32cm
one side of this square = 32/4 = 8
area of this square = 8*8 = 64
area of square whose area is equal to the sum of these two = 225 +64 = 289
one side of this square will be underroot of 289 i.e. 17
to caculate the length of the diagonal we consider any one of the triangles made by the diagonal.
using pythagoras theorem, we get
17square +17 square = diagonal square
289+289 = diagonal square
578 = diagonal's square
therefore, diagonal will be underroot of 578
which is
24.09
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