Math, asked by adityachallenger18, 5 hours ago

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​

Answers

Answered by Anonymous
0

 \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

–        –        –  

▬▬▬▬▬▬▬▬▬▬▬▬

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.

\huge\boxed{\dag\sf\red{Thanks}\dag}

Answered by dassrijani1610
1

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.

Attachments:
Similar questions