Question

two square have sides x cm and (x+4) cm. the sum of their areas is 656 cm square. find the sides of the squares.

Answer 1

${(x)}^{2} + {(x + 4)}^{2} = 656 \\ {x}^{2} + {x}^{2} + 16 + 8x = 656 \\ 2 {x}^{2} + 16 + 8x = 656 \\ {2x}^{2} + 8x = 640 \\ 2x(x + 4) = 640 \\ x(x + 4) = 320$
now, putting 16 in place of x,we get-
$16(16 + 4) = 320 \\ 16 \times 20 = 320 \\ 320 = 320$
therefore,x=16 and sides are 16 and 20

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Here we have,

As we know that :-

Area of square = a²

(Here a² = side of square)

Given,

$\textbf{\underline{Two\;squares\;of\;sides}}$

= (x , x + 4)

Now,

$\textbf{\underline{Area\;of\;square :-}}$

= (x)²

Hence we get

$\textbf{\underline{Area\;of\;square :-}}$

= x² cm²

Now,

Again

$\textbf{\underline{Area\;of\;square :-}}$

= (x + 4)²

Now,

We know that

(a + b)² = a² + b² + 2ab

Area of square of side x cm

(x² + 4 + 8x)

(x + 4) = x² + 16 + 8x

Also,

${\boxed{\sf\:{Sum\;of\;area\;of\;both\;squares = 656 cm^2}}}$

x + x + 4 = 656 cm²

x² + x² + 16 + 8x = 656 cm²

2x² + 16 + 8x = 656

2x² + 8x + 16 - 656 = 0

2x² + 8x - 640 = 0

x² + 4x - 320 = 0

Now,

x² + (20 - 16)x - 320 = 0

x² + 20x - 16x - 320

x(x + 20) - 16(x + 20) = 0

(x + 20)(x - 16) = 0

Hence,

x + 20 = 0

x = - 20

Also,

x - 16 = 0

x = 16

$\textbf{\underline{(Negative\;value\;is\;not\; applicable)}}$

x = 16

$\textbf{\underline{Length\;of\;sides\;of\;squares}}$

x = 16 cm

x + 4 = 16 + 4 = 20 cm