Question

a piece of wire is 20 cm. long. it is cut into pieces, each of which is then bent to form a square. the total area of the two squares is 13 sq. cm. How long is side of each square?

Answer 1

If the squares have sides a and b, then we have
4a+4b=20
a^2+b^2 = 13

a+b=5
(a+b)^2 = 25
a^2+b^2+2ab = 13+2ab = 25
2ab=12
ab=6
If we assume integer sides, then since the factors of 6 are 2 and 3,
a=2, b=3.
check:
4*2+4*3 = 20
2^3+3^2 = 13
OK