If twice the area of a smaller square is subtracted from the area of a larger square, the result is $14 {c m}^{2}$ . However, if twice the area of the larger square is added to three times the area of the smaller square, the result is $203 {c m}^{2}$ . Determine the sides of the square.

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Solution

Let the lengths of each side of the smaller square be $x$ cm and that of the larger square be $y$ cm.
Then, area of the smaller square $= x^{2}$ ${c m}^{2}$

$y^{2} - 2 x^{2} = 14.... (i)$
$2 y^{2} + 3 x^{2} = 203.... (i i)$

From (i) we have
$y^{2} = 14 + 2 x^{2}$

Substituting this value of $y^{2}$ in (ii) we get
$\Rightarrow 28 + 4 x^{2} + 3 x^{2} = 203 \Rightarrow 7 x^{2} = 203 - 28$

$\Rightarrow 7 x^{2} = 175 \Rightarrow x^{2} = 25 \Rightarrow x = 5 c m$

Putting $x = 5$ in (i) we get

$y^{2} - 2 \times 5^{2} = 14 \Rightarrow y^{2} = 64 \Rightarrow y = 8$

Hence the lengths of the sides of the square are $5 c m$ and $8 c m$ respectively

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If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14cm2. However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203cm2. Determine the sides of the square.

If twice the area of a smaller square is subtracted from the area of a larger square, the result is $14 {c m}^{2}$ . However, if twice the area of the larger square is added to three times the area of the smaller square, the result is $203 {c m}^{2}$ . Determine the sides of the square.