# The diagonal of the rectangle is 10cm and its perimeter is 28cm. Find the side of the rectangle.

September 14, 2021 | education

| 1. Vertices of the rectangle A, B, C, D. AC – diagonal.

2. We take the length of the side of the CD for x, the length of the side of the blood pressure for y.

3. Let’s compose two equations:

(1) x ² + y ² = AC² (by the Pythagorean theorem); x² + y² = 100;

(2) 2x + 2y = 28; x + y = 14; x = 14 – y;

4. Substitute the value x = 14 – y into the first equation:

(14 – y) ² + y² = 100;

196 – 28y + y² + y² = 100;

2u² – 28x + 96 = 0;

y² – 14x + 48 = 0;

The first value y = (14 + √196 – 48 x 4) 2 = (14 + 2) / 2 = 8 cm.

The second value is y = (14 – 2) / 2 = 6 cm.

5. The first value is x = 14 – 8 = 6 cm. The second value is x = 14 – 6 = 8 cm.

Answer: the length of the CD side can be 8 cm or 6 cm, the length of the AD side can be

equal to 6 cm or 8 cm.