Find the measurements of the rectangle, bearing in mind that its perimeter is: 46 cm and the diagonal is 17 cm.

Let’s denote the length of this geometric figure through x, and the width of this rectangle through y.

In the initial data for this task, it is reported that if you add up the lengths of all sides of a given geometric figure, the result will be 46 cm, therefore, the following relationship holds:

2x + 2y = 46.

Since the length of the diagonal of this rectangle is 17 cm, using the Pythagorean theorem, we obtain the following equation:

x ^ 2 + y ^ 2 = 17 ^ 2.

Substituting into the second equation the value x = 23 – y from the first equation, we get:

(23 – y) ^ 2 + y ^ 2 = 289;

y ^ 2 – 46y + 529 + y ^ 2 = 289;

2y ^ 2 – 46y + 529 – 289 = 0;

2y ^ 2 – 46y + 240 = 0;

y ^ 2 – 23y + 120 = 0;

y = (23 ± √ (529 – 4 * 120)) / 2 = (23 ± √ (529 – 480)) / 2 = (23 ± √49) / 2 = (23 ± 7) / 2;

y1 = (23 + 7) / 2 = 30/2 = 15;

y2 = (23 – 7) / 2 = 16/2 = 8.

Find x:

x1 = 23 – y1 = 23 – 15 = 8;

x2 = 23 – y2 = 23 – 8 = 15.

Answer: 8 cm and 15 cm.