Question

Sum of the areas of two squares is 400 cm². If the difference of their perimeters is 16 cm, find the sides of the two squares.

Answer 1

Answer:

400/16

25cm2

iska square root

5

Answer 2

$\huge \bf{ \underline{ \overline{ \mid{ \bold \red{Answer - }} \mid}}}$

$\underline{ \underline{ \bold{Given - }}}$

Sum of areas of two squares =400 cm²

Difference of their perimeters =16 cm

Now,

Let the side of the given squares be $a$cm and $b \:$cm. Then,

${a}^{2} + {b}^{2} = 400 .......(1)\\ and \: 4a - 4b = 16 \implies \: a - b = 4........(2)$

Squaring (2) on both sides, we get

${(a - b)}^{2} = 16 \implies \: ( {a}^{2} + {b}^{2} ) - 2ab = 16 \: \\ \implies400 - 2ab = 16 \: \: using \: (1) \\ \implies2ab \: = 384 \implies \: ab = 192 \: \: \: ....(3)$

Now,

$( {a + b})^{2} - ( {a - b)}^{2} = 4ab \\ \implies \: ( {a + b)}^{2} - 16 = 4 \times 192 \\ \implies \: ( {a + b)}^{2} = 768 + 16 = 784 \\ \implies \: a + b = \sqrt{784} = 28$

Now, on solving$a + b = 28 \: and \: a - b = 4$

$</p><p>\therefore \: a = 16cm \: and \: b = 12cm$

Hence the sides of the given squares are 16 cm and 12 cm.