A rectangle has a perimeter 40cm and the area is 51cm (squared). Find the dimensions of the rectangle?

Question

Plz help with working outs!!! I will give best answer

Answer 1

Since the area is 51 cm^2 it should be a product of two numbers. Only 17 and 3 are the factors of 51. And they are correct because 17 + 3 = 20 and two times of that is the perimeter = 40 cm. OK, now let us do it in a conventional way:

Let a and be the two sides of the rectangle and we have 2a + 2b = 40 or a + b = 20 and a X b = 51

Let us substitute for b = 20 - a in the second equation and we get

a.(20 - a) = 51 or 20 a - a^2 = 51 or
a^2 - 20a + 51 = 0 which can be written as (a - 17) (a - 3) = 0 so we get a = 17 and 3. If a = 17, b = 3 and vice versa.

Answer 2

i.e 2(a+b)=40 and a*b=51.
solving we get, a=17 and b=3 or a=3 and b=17.