Question

If the side of a square is increased by 4 cm ,its area increased by 32cm² find the side of the Square.​

Answer 1

Answer:

Side of the square = 2cm

Given:

• If side of the square is increased by 4 cm, the area will increase by 32 cm²

To Find:

• The side of the square.

Solution:

let the side of the square = x

Area of the square = side × side

= x × x = x²

Area of the square is x²

[ Now we will take the square of x + 4 be equal to 32cm² added to the area of the square ]

[ For the ease of calculations, we won't use units such as cm or cm², we will add them later ]

According to the question:

$\rm\implies \: {(x + 4)}^2 = x^2 + 32$

$\rm\implies x^2 + 8x + 16 = x^2 + 32$

$\rm\implies{\not{ x^2}} + 8x + 16 = {\not{x^2}} + 32$

$\rm\implies 8x + 16 = 32$

$\rm\implies 8(x + 2) = 32$

$\rm\implies x + 2 = \dfrac{32 }{8}$

$\rm\implies x + 2 = 4$

$\rm\implies x = 4 - 2$

$\rm\implies x = 2$

The side of the square is 2cm.

Answer 2

$\huge\bold{\mathbb{QUESTION}}$

If the side of a square is increased by $4\:cm,$ its area increased by $32\:cm^{2}.$ Find the side of the square.

$\huge\bold{\mathbb{GIVEN}}$

If the side of a square is increased by $4\:cm,$ its area increased by $32\:cm^{2}.$

$\huge\bold{\mathbb{TO\:FIND}}$

The side of the square.

$\huge\bold{\mathbb{SOLUTION}}$

Let the side of the square be $x\:cm.$

We know that:

$\boxed{\large{Area\: of\: square=Side\times Side}}$

So, area of the square

$=(x\times x) =x^{2}$

Given that if the side of a square is increased by $4\:cm,$ its area increased by $32\:cm^{2}.$

So, length of new sides of the square

$\:\:\:\:\:\:\:\:\:\:\:\:\: = (x+4)\:cm$

And, new area of the square

$\:\:\:\:\:\:\:\:\:\:\:\:\: = (x^{2}+32)\:cm^{2}$

Now we can say-

$(x+4)^{2}=x^{2}+32$

Using $(a+b)^{2}=a^{2}+2ab+b^{2}$,

$\implies x^{2}+(2\times x\times 4)+4^{2}=x^{2}+32$

$\implies x^{2}+8x+16=x^{2}+32$

$\implies \cancel{x^{2}}+8x+16=\cancel{x^{2}}+32$

$\implies 8x+8+16=32$

$\implies 8x=32-16$

$\implies 8x=16$

$\implies x={\dfrac{16}{8}}$

$\implies x=\cancel{{\dfrac{16}{8}}}$

$\implies x=2$

$\huge\bold{\mathbb{HENCE}}$

$x=2$

Length of side $=x\:cm=2\:cm$

$\huge\bold{\mathbb{THEREFORE}}$

The side of the square is $2\:cm.$

$\huge\bold{\mathbb{DONE}}$