Question

If the twice area of a smaller square is subtracted from the area of larger square the result is 14cm^2 however if the twice the area of larger square is added to 3 times of the area of smaller , the result is 203 cm^2 . Determine the sides of two square​

Answer 1

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• If the twice area of a smaller square is subtracted from the area of larger square the result is 14cm^2 however if the twice the area of larger square is added to 3 times of the area of smaller , the result is 203 cm^2 . Determine the sides of two square

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• Let the side of smaller square = x cm
• and side of bigger square = y cm

According to the condition,

${y}^{2} – 2 {x}^{2} = 14               ...(i)$

$and \: 2 {y}^{2} + 3 {x}^{2} = 203   ...(ii)$

Multiply (i) by 2 and (ii) by 1

$2 {y}^{2} – 4 {x}^{2} = 28$

$2 {y}^{2} + 3 {x}^{2} = 203$

–        –        –  

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Subtracting, we get, –7x²= -175

$= {x}^{2} = \frac{ - 175}{ - 7} = 25$

${x}^{2} – 25 = 0$

$⇒ (x + 5)(x - 5) = 0$

$Either \: x + 5 = 0,$

$then \: x = –5,$

$but \: it \: is \: not \: possible$

$or$

$x – 5 = 0,$

$then \: x = 5.$

Substitute the value of

x in (i)

${y}^{2} – 2 {(5)}^{2} = 14$

$⇒ {y}^{2} = 14 + 2 \times 25$

${y}^{2} = 14 + 50 = 64$

$= {(8)}^{2}$

$∴ y = 8$

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Hence side of the smaller

square = 5 cm

and

side of bigger square = 8 cm.

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Answer 2

Answer:

1. side of smaller square = 5 cm
2. side of smaller square = 5 cmside of larger square = 8 cm

Step-by-step explanation:

STEPS ARE IN ATTACHMENT.