Question

When the sides of a square are increased by 4. area become 256. What is the length of a
side of the first square ?​

Answer 1

Solution :-

Let :-

Side of first square = x

Side of second square = x + 4

According to the question  :-

-$\longrightarrow \sf (x+4)^2 = 256 \\\\\longrightarrow x^2+4^2+2 \times 4 \times x = 256 \\\\\longrightarrow x^2+16+8x = 256 \\\\\longrightarrow x^2+8x = 256-16 \\\\\longrightarrow x^2+8x = 240 \\\\\longrightarrow x^2+8x - 240 = 0 \\\\\longrightarrow x^2+20x- 12x-240 = 0 \\\\\longrightarrow x(x+20)-12(x+20) = 0 \\\\\longrightarrow (x+20)(x-12) = 0 \\\\\longrightarrow \bf x = -20 \ , \ x= 12$

Side of a square cannot be negative.

So, x = 12

Side of the first square = 12 cm

Answer 2

$\red\bigstar$ Correct Question:

• When the sides of a square are increased by 4, then the area becomes 256. What is the length of the side of the square ?

$\pink\bigstar$Answer:

• x = 12

$\blue\bigstar$Given:

• The sides of a square are increased by 4
• After the sides are increased, the area becomes 256

$\red\bigstar$To find:

• Length of the side of the square

$\pink\bigstar$ Solution:

Let the side of the square be x.

New side of the square = ( x + 4 )

We know that,

$\star$Area of a square = (Side)²

So, by substituting the values, we get :

256 = (x + 4)²

$\implies$ x² + 2 × x × 4 + (4)² = 256

(By using (a + b)² = a² + 2ab + b²)

$\implies$ x² + 8x + 16 = 256

$\implies$ x² + 8x = 256 - 16

$\implies$ x² + 8x = 240

$\implies$ x² + 8x - 240 = 0

Here, we have to use middle term splitting i.e.

• x² + (a + b)x + ab

So in x² + 8x - 240 = 0,

• Sum = 8
• Product = (- 240)

Now,

• Sum = 8 = 20 - 12
• Product = (- 240) = 20 × (-12)

$\therefore$x² + 8x - 240 = 0

$\implies$x² + 20x - 12x - 240 = 0

$\implies$ x ( x + 20) - 12 (x + 20) = 0

$\implies$ (x + 20) (x - 12) = 0

(By taking ( x + 20 ) as common)

$\star$ Case 1 :

x + 20 = 0

$\implies$ x = (-20)

$\star$ Case 2 :

x - 12 = 0

$\implies$ x = 12

$\because$We know that length cannot be negative,

$\implies$ $\boxed{\sf x \:= \:12 \:}$

$\green\bigstar$ Concepts Used:

• Assumption of unknown values

• Area of a square = (Side)²

• Substitution of values

• (a + b)² = a² + 2ab + b²

• Transposition Method

• Middle Term splitting method