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The diameter of circumcircle of a rectangle is 10 cm and breadth of the rectangle is 6 cm. Its length is
- a)6 cm
- b)5 cm
- c)8 cm
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The diameter of circumcircle of a rectangle is 10 cm and breadth of th...
Breadth=6 cm,circumcircle diameter=10cm this is the diameter of rectangle . then use phythagoures theorem then we get length=8cm
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The diameter of circumcircle of a rectangle is 10 cm and breadth of th...
Given:
- Diameter of the circumcircle of a rectangle = 10 cm
- Breadth of the rectangle = 6 cm
To find:
- Length of the rectangle
We know that a rectangle has opposite sides equal in length and opposite angles equal in measure. In a rectangle, the diagonals are equal and bisect each other.
Therefore, the diameter of the circumcircle is equal to the length of the rectangle's diagonal.
Let's assume the length of the rectangle is 'x' cm.
From the given information, we can draw the following diagram:
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|_____________________|
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The rectangle is inscribed in the circle, so the diagonal of the rectangle is the diameter of the circle.
We can apply the Pythagorean theorem to find the length of the diagonal (diameter) of the rectangle:
Length of diagonal (diameter)^2 = Length^2 + Breadth^2
10^2 = x^2 + 6^2
100 = x^2 + 36
x^2 = 100 - 36
x^2 = 64
Taking the square root on both sides:
x = √64
x = 8 cm
Therefore, the length of the rectangle is 8 cm.
Hence, the correct answer is option C) 8 cm.
- Diameter of the circumcircle of a rectangle = 10 cm
- Breadth of the rectangle = 6 cm
To find:
- Length of the rectangle
We know that a rectangle has opposite sides equal in length and opposite angles equal in measure. In a rectangle, the diagonals are equal and bisect each other.
Therefore, the diameter of the circumcircle is equal to the length of the rectangle's diagonal.
Let's assume the length of the rectangle is 'x' cm.
From the given information, we can draw the following diagram:
```
---------------------
| |
| |
| |
| |
| |
| |
| |
| |
| |
|_____________________|
```
The rectangle is inscribed in the circle, so the diagonal of the rectangle is the diameter of the circle.
We can apply the Pythagorean theorem to find the length of the diagonal (diameter) of the rectangle:
Length of diagonal (diameter)^2 = Length^2 + Breadth^2
10^2 = x^2 + 6^2
100 = x^2 + 36
x^2 = 100 - 36
x^2 = 64
Taking the square root on both sides:
x = √64
x = 8 cm
Therefore, the length of the rectangle is 8 cm.
Hence, the correct answer is option C) 8 cm.
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The diameter of circumcircle of a rectangle is 10 cm and breadth of the rectangle is 6 cm. Its length isa)6 cmb)5 cmc)8 cmd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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