Question

If two opposite sides of a square are increased by 12 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 66 square meters. Find the area of the original square.

Answer 1

100

Step-by-step explanation:

Let us Assume x as the original sides of the square

As we know that

Area of rectangle is

`= Length * width`

where,

Length is 12 meters

And, the width is 7 meters

Moreover, the area of the rectangle is 66 square meters

Now since the length is increased by 12 meters and the width is decreased by 7 meters

So, the equation would be

(x + 12) (x - 7) = 66

x^2 + 5x - 84 = 66

x^2 + 5x - 150 = 0

Now, we compute the factor of the above equation

(x - 10) (x + 15) = 0

We do not consider the negative root

Therefore the area of original square is

= Side^2

= 10^2

= 100