F.4 Maths

(a) The total lenght of the square with side x = 4x
The length of the other wire = 80 - 4x
The side of this square = (80 - 4x)/4 = 20 - x
The total area = x^2 + (20 - x)^2
= x^2 + 400 - 40x + x^2
= 2x^2 - 40x + 400 cm^2
(b) Area = 2x^2 - 40x + 400
= 2(x^2 - 20x + 100) + 200
= 2(x - 10)^2 + 200
Area is minimum whenx = 10
The sides of the squares are 10cm and 20 - x = 10 cm