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The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of the longer diagonal?
- a)4/5
- b)2/5
- c)3/4
- d)1/4
Correct answer is option 'B'. Can you explain this answer?
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The length of one diagonal of a rhombus is 80% of the other diagonal. ...
Let length of the longer diagonal = x cm
Then, length of other diagonal
Then, length of other diagonal
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The length of one diagonal of a rhombus is 80% of the other diagonal. ...
Given:
- The length of one diagonal of the rhombus is 80% of the other diagonal.
To find:
- The area of the rhombus in terms of the square of the length of the longer diagonal.
Solution:
Let's assume that the longer diagonal of the rhombus is 'd' units.
Step 1: Finding the length of the other diagonal
Since the length of one diagonal is 80% of the other diagonal, we can calculate the length of the other diagonal as follows:
Length of the other diagonal = 80/100 × d = 0.8d
Step 2: Finding the area of the rhombus
The area of a rhombus can be calculated using the formula:
Area = (1/2) × (Product of diagonals)
Since the diagonals of the rhombus are perpendicular bisectors of each other, the product of the diagonals is equal to the product of their lengths:
Area = (1/2) × d × 0.8d = 0.4d^2
Step 3: Expressing the area in terms of the square of the length of the longer diagonal
We need to find the area of the rhombus in terms of the square of the length of the longer diagonal (d^2).
So, let's express the area we found in the previous step in terms of d^2:
Area = 0.4d^2 = 0.4 × (d × d) = 0.4 × d^2
Conclusion:
The area of the rhombus is 0.4 times the square of the length of the longer diagonal.
Therefore, the correct answer is option 'B' - 2/5.
- The length of one diagonal of the rhombus is 80% of the other diagonal.
To find:
- The area of the rhombus in terms of the square of the length of the longer diagonal.
Solution:
Let's assume that the longer diagonal of the rhombus is 'd' units.
Step 1: Finding the length of the other diagonal
Since the length of one diagonal is 80% of the other diagonal, we can calculate the length of the other diagonal as follows:
Length of the other diagonal = 80/100 × d = 0.8d
Step 2: Finding the area of the rhombus
The area of a rhombus can be calculated using the formula:
Area = (1/2) × (Product of diagonals)
Since the diagonals of the rhombus are perpendicular bisectors of each other, the product of the diagonals is equal to the product of their lengths:
Area = (1/2) × d × 0.8d = 0.4d^2
Step 3: Expressing the area in terms of the square of the length of the longer diagonal
We need to find the area of the rhombus in terms of the square of the length of the longer diagonal (d^2).
So, let's express the area we found in the previous step in terms of d^2:
Area = 0.4d^2 = 0.4 × (d × d) = 0.4 × d^2
Conclusion:
The area of the rhombus is 0.4 times the square of the length of the longer diagonal.
Therefore, the correct answer is option 'B' - 2/5.
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The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of the longer diagonal?a)4/5b)2/5c)3/4d)1/4Correct answer is option 'B'. Can you explain this answer?
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