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

Step-by-step explanation:

Let the side of original square be x

If the side is increased by 4

The length becomes = x + 4

Given, Area of the square = 256

As, we know that:-

Area of a square = (side)²

$\sf \longrightarrow (x + 4)^2 = 256$

$\sf \longrightarrow {x}^{2} +2(x)(4) + {4}^{2} = 256$

$\sf \longrightarrow {x}^{2} +8x + 16= 256$

$\sf \longrightarrow {x}^{2} +8x + 16 - 256 = 0$

$\sf \longrightarrow {x}^{2} +8x - 240= 0$

Now, Factorise the equation by splitting the middle term:-

$\sf \longrightarrow {x}^{2} +20x - 12x - 240= 0$

$\sf \longrightarrow x(x+20) - 12(x + 20)= 0$

$\sf \longrightarrow (x+20) (x - 12)= 0$

$\sf \longrightarrow x+20 = 0 \: \: \: (or) \: \: \: x - 12= 0$

$\sf \longrightarrow x = - 20 \: \: \: (or) \: \: \: x = 12$

Since, The side of a square cannot be negative.

$\sf x \not= -20$

$\sf \longrightarrow x = 12$

Therefore:-

Side of the original square = 12 units