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

Answer:

Let the side of the smaller square = a cm

side of the larger square = b cm

twice the area of a smaller square is subtracted from the area of the larger

square =14 cm²

b² - 2a² =14-----(1)

twice the area of the larger square is add to three times the area of the smaller square =203 cm²

2b² + 3a²=203---(2)

multiply (1) with 2 and subtract it from (2)

2b²+3a²=203

2b²-4a²= 14

____________

7a²=175

a²= 175/7

a²=25

a = 5 cm

substitute a =5 in (1)

b²-2a²=14

b²-2*5²=14

b²-50=14

b²=14+50

b²=64

b=8 cm

larger square side = b =8cm

smaller square side = a = 5 cm

Answer 2

$\red{ \qquad \underline{ \pmb{{ \mathbb{ \maltese  \:  COMPLETE \: \: QUESTION \:   \maltese }}}}}$

• 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

$\large \mathfrak{ \text{W}e \: \text{K}now }$

$\Large \orange{\qquad \underline{ \pmb{{ \mathbb{ \maltese  \:SOLUTION \:  \maltese }}}}}$

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)

${y}^{2} – 2 {(5)}^{2} = 14$

$⇒ {y}^{2} = 14 + 2 \times 25$

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

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

$∴ y = 8$

$\huge\fbox\pink{✯Answer✯}$

$\purple{\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese  \:  REQUIRED \: \: INFO \:  \maltese }}}}}$

Hence side of the smaller

square = 5 cm

and

side of bigger square = 8 cm.