Question

sum of areas is 305m^2 if difference of their perimeter is 36 cm find side of two square
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Answer 1

Step-by-step explanation:

sum of areas of two square = 305

difference of perimeter of the squares = 36

let side of one square be x and side of other square be y

area of 1st square = x²

area of 2nd square = y²

sum of the areas

x² + y² = 305 equ (1)

perimeter of first square = 4x

perimeter of 2nd square = 4y

difference between the perimeter

4x - 4y = 36

4(x - y) = 36

x - y = 36/4

x - y = 9

x = 9 + y equ (2)

substitute x = 9 + y in equ (1)

${x}^{2} + {y}^{2} = 305 \\ {(9 + y)}^{2} + {y}^{2} = 305 \\ 81 + 18y + {y}^{2} + {y}^{2} = 305 \\ 2 {y}^{2} + 18y = 305 - 81 \\ 2 {y}^{2} + 18y = 224 \\ 2{y}^{2} + 18y - 224 = 0 \\ 2( {y}^{2} + 9y - 112) = 0 \\ {y}^{2} + 9y - 112 = 0 \\ {y}^{2} + 16y - 7y - 112 = 0 \\ y(y + 16) - 7(y + 16) = 0 \\ (y + 16)(y - 7) = 0 \\ y + 16 = 0 \: \: \: \: y - 7 = 0 \\ y = - 16 \: \: \: \: \: \: \: \: y = 7$

we take y = 7 as side of square cannot be negative

from equ (2)

x = 9 + y

x = 9 + 7

x = 16

therefore the sides the squares

side of first square = x = 16 m

side of second square = y = 9 m

Hope you get your answer