Geometry Problem
Given information:
- Length of the larger side of the rectangle: 13.5 cm
- Length of the diagonal: 9/3 cm
- Angle formed between the diagonal and the smaller side: 60 degrees
To find:
- Length of the smaller side of the rectangle
- Area of the rectangle
Solution:
- Let's denote the length of the smaller side of the rectangle as "x" cm.
- Using the given information, we can form a right triangle with the diagonal as the hypotenuse, the smaller side as the adjacent side, and the angle between them as 60 degrees.
- Using trigonometric ratios, we can determine the length of the smaller side:
- Cosine of the angle = Adjacent side / Hypotenuse
- Cos(60 degrees) = x / (9/3 cm)
- Simplifying, we get: 1/2 = x / (3 cm)
- Cross-multiplying, we get: x = 3/2 cm
- Therefore, the length of the smaller side of the rectangle is 3/2 cm.
- To find the area of the rectangle, we can use the formula: Area = Length * Width
- Length = 13.5 cm
- Width = 3/2 cm
- Area = 13.5 cm * (3/2 cm)
- Simplifying, we get: Area = 27/2 cm^2
- Therefore, the area of the rectangle is 27/2 cm^2, or 13.5 cm^2.
Answer:
- Length of the smaller side of the rectangle: 3/2 cm
- Area of the rectangle: 27/2 cm^2
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