Here, area is given in terms of a quadratic expression in one varaible. To find the possible length and breadth of a rectangle, we have to factorise the given expression.
Area=25a2−35a+12 (Area=l× b)=25a2−20a−15a+12(splitting middle term)=5a(5a−4)−3(5a−4)=(5a−4)(5a−3)
Since Length is greater than breadth, 5a−3 is the length and 5a−4 is the breadth.
When a=4,
Length =5a−3=5(4)−3=17
Breadth =5a−4=5(4)−4=16
Perimeter =2((5a−3)+(5a−4))=2(17+16)=66 units
Area =(5a−3)(5a−4)=17×16=272 sq units.