Question

sum of the area of two squares is 484 meter square and the sum of their perimeter is 64 find the sides of the squares​

Answer 1

Step-by-step explanation:

Let the side of square 1 be X and that of square 2 be Y

$Then \: area \: of \: square1 \: is \: \: {x}^{2} </p><p>$

$and \: area \: of \: \: square2 \: is \: {y}^{2} </p><p>$

Similarly

$perimeter \: of \: square1 \: is \: 4x</p><p>$

Also,

$perimeter \: of \: square2 \: is \: 4y$

Given

${x}^{2} + {y}^{2} = 484 \: \: \: \: \: \: \: \: \: \: \: (1)$

$4x + 4y = 64$

$x = 16 - y$

substituting the above in eqn (1)

${(16 - y)}^{2} + {y}^{2} = 484$

${y}^{2} + 256 - 32y + {y}^{2} = 484$

$2 {y}^{2} - 32y - 228 = 0$

${y}^{2} - 16y - 114 = 0$

Solving the equation we get

$y = 8 + \sqrt{178 } \: and \: y = 8 - \sqrt{178}$

similarly,

$x = 8 - \sqrt{178} \: and \: 8 + \sqrt{178}$