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The area of a rhombus is 200 cm², and one of its diagonals is 20 cm. The length of the other diagonal is _____
- a)20 cm
- b)20 m
- c)22 cm
- d)22 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The area of a rhombus is 200 cm², and one of its diagonals is 20 ...
Let the length of one diagonal be d1 = 20 cm, and the length of the other diagonal be d2
The formula for the area of a rhombus is:
Area = 1/2 x d1 x d
Area = 1/2 x d1 x d
2
Substitute the given values:
200 cm² = 1/2 x 20 x d2
200 cm² = 10 x d2
20cm = d2
Most Upvoted Answer
The area of a rhombus is 200 cm², and one of its diagonals is 20 ...
Understanding the Area of a Rhombus
The area of a rhombus can be calculated using the formula:
- Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals.
Given Information
- Area = 200 cm²
- One diagonal (d1) = 20 cm
Finding the Other Diagonal
To find the length of the second diagonal (d2), we can rearrange the area formula:
- 200 = (20 * d2) / 2
Now, let's solve for d2:
- First, multiply both sides by 2:
- 400 = 20 * d2
- Next, divide both sides by 20:
- d2 = 400 / 20
- d2 = 20 cm
Conclusion
The length of the other diagonal (d2) is 20 cm.
Final Answer
The correct answer is option 'A' (20 cm).
This shows that both diagonals of the rhombus can be equal, which is a special case where the rhombus is also a square.
The area of a rhombus can be calculated using the formula:
- Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals.
Given Information
- Area = 200 cm²
- One diagonal (d1) = 20 cm
Finding the Other Diagonal
To find the length of the second diagonal (d2), we can rearrange the area formula:
- 200 = (20 * d2) / 2
Now, let's solve for d2:
- First, multiply both sides by 2:
- 400 = 20 * d2
- Next, divide both sides by 20:
- d2 = 400 / 20
- d2 = 20 cm
Conclusion
The length of the other diagonal (d2) is 20 cm.
Final Answer
The correct answer is option 'A' (20 cm).
This shows that both diagonals of the rhombus can be equal, which is a special case where the rhombus is also a square.
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