if 4 times the area of a smaller square is subtracted from the area of a larger square,the result is 144m^2 The sum of the areas of the two squares is 464 m^2 Determine the sides of the two squares.
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if 4 times the area of a smaller square is subtracted from the area of a larger square,the result is 144m^2 The sum of the areas of the two squares is 464 m^2 Determine the sides of the two squares.
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And side of larger square is (√a) m
Hence, Area of smaller square is ( b ) m^2 and Area of larger square is ( a ) m^2
Given, 4 times the area of smaller square - area of larger square = 144 m^2
a - 4 ( b ) = 144 m^2
a - 4b = 144
a = 144 + 4b ----1equation
Sum of areas of squares = 464 m^2
a + b = 464
Putting the value of a from 1equation,
=> 4b + 144 + b = 464
=> 5b = 464 - 144
=> 5b = 320
=> b = 64
Putting the value of ( b ) in 2equation,
=> a + b = 464
=> a + 64 = 464
=> a = 464 - 64
=> a = 200
Hence,
Area of smaller square is b = 64 m^2
Therefore, side of smaller square is (√64 m^2) => 8 m
Area of larger square is a = 400 m^2
Therefore, side of larger square is (√400 m^2) => 20 m