Question

If the area of a rectangle is a${}^2$ + 5ab + 6b${}^2$, what will be its perimeter? (2 marks)

Answer 1

Area of the rectangle = a${}^2$ + 5ab + 6b${}^2$
= a${}^2$ + 2ab + 3ab + 6b${}^2$
= a(a + 2b) + 3b(a + 2b)
= (a + 2b)(a + 3b) (1 mark)
So, the length and breadth of the rectangle will be (a + 2b) and (a + 3b) respectively.
Perimeter of the rectangle = 2 × (Length + Breadth)
= 2(a + 2b + a + 3b)
= 2(2a + 5b)
= 4a + 10b
(1 mark)