A piece of wire 100 cm long is cut into two pieces, and then each piece is bent into a shape of a square. Find the length of each piece of wire if the sum of the enclosed areas is 397 cm2.

Answer 1

a wire is 100 cm long

cut it in two pieces, x and 100-x in lengths

make x into a square with 4 sides each x/4

make 100-x into a square with 4 sides each (100-x)/4

find the area of each square

(x/4)^2 and [(100-x)/4]^2

sum them to get 397 cm^2

expand and solve for x

(x/4)^2 + [(100-x)/4]^2 = 397

x^2/16 + (100^2 -200x + x^2)/16 = 397

2x^2 -200x +10000 = 16(397) = 6352

2x^2 -200x = 6352 -10000 = -3648

x^2 - 100x =-3648/2 =-1824

x^2 -100x + 50^2 =-1824 + 50^2

(x-50)^2 = 2500-1824 = 676

x-50 = + or -sqr676 = + or - 26

x = 76 or 24

the two pieces of wire are 76 cm and 24 cm

76/4 = 19

24/4 = 6

19^2 + 6^2 = 361+36 = 397