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.
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