Question

8. Two squares have sides x cm and (x + 4) cm.
The sum of their areas is 656 sq. cm. Express
this as an algebraic equation in x and solve the
equation to find the sides of the squares.​

Answer 1

Answer:

16 cm , 20 cm

Step-by-step explanation:

$x^{2}$ + $(x + 4)x^{2}$ = 656

$2x^{2}$ + $8x$ + 16 = 656

$2x^{2}$ + $8x$ = 656 - 16

$2x^{2}$ + $8x$ = 640

$x^{2}$ + $4x$ = 640/2

           = 320

$x + 2^{2}$ = 320 + 4

          = 324

($x+2^{2}$) = $\sqrt{324}$

           = $18^{2}$

length cannot be negative so,

$x+2 = 18$

x = 18 - 2

  = 16 cm

$(x+4)$ = 16+4 = 20 cm

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Answer 2

Answer:

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Applying the above condition, we get

${x}^{2} + ( {x + 4})^{2} = 656$

${2x}^{2} + 8x + 16 = 656$

${2x}^{2} + 8x - 640 = 0$

${x}^{2} + 4x - 320 = 0$

$( {x + 4})^{2} = 324$

$( {x + 2})^{2} = {18}^{2}$

Now length cannot be negative, hence

$x + 2 = 18$

$x = 16$

$x + 4 = 20cm$

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