The perimeter of the rectangle is 46cm and its diagonal is 17cm. find the larger side of the rectangle.

Let one of the dimensions of the rectangle be equal to the variable a.
Then its other size can be represented in the form 46: 2 – a = 23 – a.
Since we know from the condition that its diagonal is 17 cm, then it is possible to draw up an equation and find out what the large side is:
a ^ 2 + (23 – a) ^ 2 = 172;
a ^ 2 + 529 – 46a + a ^ 2 = 289;
a ^ 2 – 23 a + 120 = 0;
D = 529 – 4 * 120 = 49 = 72;
a1 = (23 – 7): 2 = 8;
a2 = (23 + 7): 2 = 15;
15> 8.
Answer: The large side of the rectangle will be 15 centimeters.