Respuesta :
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)
[tex]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[/tex]
⇒ 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.
