ANCIENT BABYLONIA 20021000 BCE The sum of the area of two sq

ANCIENT BABYLONIA (2002-1000 BCE) The sum of the area of two squares is 1525. The side of the second square is two-thirds that of the first plus 5 units. Find the sides of each square A sir le contains an inscribed triangle

Solution

Let the side of the first square be x

Let the side of the second square be y

x^2 + y^2 = 1525 ---- (i)

y = 2/3x + 5

x^2 + (2/3x + 5)^2 = 1525

x^2 + 4/9x^2 + 25 + 20/3x = 1525

13/9x^2 + 20/3 *x - 1500 = 0

x = 30

y = 2/3 * x + 5 = 2/3 * 30 + 5 = 24

Hence the sides of the square are 30 units and 25 units