Answer:
Factor of 1,120 are
=2 × 2 × 2 × 2 × 2 ×5 × 7
So, we have to find dimensions of Length and Breadth , such that area of game board is 1,120 square inches.
There are many possible dimensions.
We will find the dimension of card board in terms of natural numbers such that difference between Length and breadth is Least.
One of the Possible Dimension can be
Length =7 × 5=35 inches
Breadth=2×2×2×2×2=32 inches
Other Possible dimension can be
Length=5×2×2×2=40
Breadth=7×2×2=28
So, selecting those dimension in which difference between Length and Breadth is Least
Length =35 inches
Breadth=32 inch
Expressing it in terms of , x
→Let ,Breadth =x inches
→Length =(x+3) inches
⇒Area of Square board which is in the shape of rectangle =Length × Breadth
→ 1120=x*(x+3)
Using Distributive property
→x²+3x=1120
→x²+3x-1120=0
