Question

A square field had 3 m added to its length ad 2 m added to its width. The field then had an area of 90 m squared. Find the length of a side of the original field.

Answer 1

Answer:

The length of a side of the original field  = 7 m.

Step-by-step explanation:

Here, the initial field is in form of a square.

Let us assume the side of the original square field = k meters

Now, the new length of the field = ( k + 3)  m

The new width of the field = ( k + 2) m

So, the new field is now a rectangle with area  = 90 sq. m

AREA OF A RECTANGLE  = LENGTH x WIDTH

Here, the area of the new field  =  New length x new width

                                                      =   ( k + 3) x ( k + 2)

$90 = ( k + 3) \times ( k + 2)\\\implies k^2 + 2k + 3k + 6 = 90\\or, k^2 + 5 k - 84 = 0\\\implies k^2 + 12k - 7k -84 = 0\\or, k (k+12) -7(k+12) = 0\\\implies (k+12)(k-7) = 0$

⇒ either (k +12) = 0 ⇒  k = -12

or, ( k-7) = 0 ⇒  k = 7

But, here k = SIDE OF A FIELD, and it CANNOT be negative.

⇒  k = 7

Hence, the length of a side of the original field  = 7 m.