Find the perimeter of the rectangle if it is known that the diagonal is 50 cm, and the sides AB: BC = 3: 4.
| April 28, 2021 | education
1. A, B, C, D – the vertices of the rectangle. P is the perimeter. VD – diagonal.
2. In a rectangle, the opposite sides are equal:
BC = AD, AB = CD.
3. By the condition of the problem AB: BC = 3: 4. Replace BC in this expression with AD:
AB: AD = 3: 4. AB = 3AD / 4.
4. AD² + AB² = BD² (by the Pythagorean theorem). We substitute here 3AD / 4 instead of AB:
AD² + (3AD / 4) ² = 2500.
AD² + 9AD² / 16 = 2500.
25AD² = 16 x 2500.
АD = √16 x 100 = 40 cm.
AB = 3 x 40: 4 = 30 cm.
5.R = 2 x 30 + 2 x 40 = 140 cm.
Answer: P = 140 cm.
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