Question

A piece of wire 40 cm long is cut into two pieces, each of which is bent to form a square. The total area of the

squares is 52 cm². Find the length of each piece.

Answer 1

24 cm and 16 cm

Explanation:

Assumed that the length of one of the wire is x cm and the other is y cm.

Given that the length of the wire = 40 cm long:

x + y = 40

x = 40 - y

Given that their total area is 52 cm²:

(x/4)² + (y/4)² = 52

x²/16 + y²/16 = 52

x² + y² = 832

Substitute x = 40 - y into x² + y² = 832:

(40- y)² + y² = 832

40² - 2(40)(y) + y² + y² = 832

1600 - 80y + 2y² = 832

2y² - 80y + 768 = 0

y² - 40y + 384 = 0

(y - 16) (y - 24) = 0

y = 16 or y = 24

if y = 16,

x = 40 - 16

x = 24

The length of one of the pieces is 24 cm and the other is 16 cm

Answer 2

Explanation:

A=s*s

A=s^2

52=s^2

s=√52

s=7.2 one side of the square

s*4 to get the four sides

7.2*4=28.8 cm length of the first piece

40-28.8=11.2cm length of the second piece