The sum of the adjacent sides of the rectangle is 17 cm, and its diagonal is 13 cm. Find the sides of the rectangle.

Let x and y be the sides of the rectangle.
x + y = 17
By the Pythagorean theorem:
x ^ + y ^ = 13 ^
Express x from the first equation and substitute it into the second:
(17 – y) ^ + y ^ = 13 ^
289 – 34 * y + 2 * y ^ = 169
y ^ – 17 * y + 60 = 0
D = 289 – 240 = 49
y1 = (17 – 7) / 2 = 5. Then x = 12.
y2 = (17 + 7) / 2 = 12. Then x = 5.
The solutions are symmetrical, we take any of them.
Answer: 5 cm, 12 cm.