Question

If the length of a square is increased by 3 cm, its area increases by 99 sq. cm.
What was the length of the square before being increased.

Answer 1

Answer:

15

Step-by-step explanation:

let actual length of square is X. Then actual area = x^2.

Now

(X+3)^2=x^2+99

x^2+9+6x=x^2+99

6x=90

X=15

Answer 2

Your question :

If the length of a square is increased by 3 cm, its area increases by 99 sq. cm.

What was the length of the square before being increased.

Explanation:

let the length of the square = X

let the area of the square

$= {x}^{2}$

After increasing the length of the square by 3 centimetre the new length of a square

= X + 3

then the new area of square

$= {(x + 3)}^{2}$

in the given question said after increasing length of a square by 3 cm the area of a square increased by 99 centimetre then the new area of square

$= {x }^{2} + 99$

we find that there are 2 area of squares one is (x+3) ^2 and the other is x square + 99

therefore (x+3) ^2 = x square + 99

(x+3)^2=x^2+99

=x^2+9+6x=x^2+99

=x^2+6x=x^2+90

=6x=90

=x=15

so length = 15