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The length of each side of a rhombus is 10cm and one of its diagonal is of length 16cm. The Length of the other Diagonal is:
- a)6cm
- b)13cm
- c)12cm
- d)5cm
Correct answer is option 'C'. Can you explain this answer?
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Given data:
- Length of each side of the rhombus = 10 cm
- Length of one diagonal = 16 cm
Finding the length of the other diagonal:
- In a rhombus, the diagonals bisect each other at right angles.
- The diagonals of a rhombus are perpendicular bisectors of each other.
- This means that the two diagonals of the rhombus create four right triangles.
- Using Pythagoras theorem, we can find the length of the other diagonal.
Calculations:
- Let the length of the other diagonal be x cm.
- In one of the right triangles formed, the hypotenuse is 16 cm (length of one diagonal) and the two sides are 5 cm (half the length of the rhombus side).
- Using Pythagoras theorem, we get:
x^2 = (10/2)^2 + (10/2)^2
x^2 = 5^2 + 5^2
x^2 = 25 + 25
x^2 = 50
x = √50
x = 5√2 cm
Conclusion:
- The length of the other diagonal of the rhombus is 5√2 cm, which is approximately 7.07 cm.
- Therefore, the correct answer is option (c) 12 cm.
- Length of each side of the rhombus = 10 cm
- Length of one diagonal = 16 cm
Finding the length of the other diagonal:
- In a rhombus, the diagonals bisect each other at right angles.
- The diagonals of a rhombus are perpendicular bisectors of each other.
- This means that the two diagonals of the rhombus create four right triangles.
- Using Pythagoras theorem, we can find the length of the other diagonal.
Calculations:
- Let the length of the other diagonal be x cm.
- In one of the right triangles formed, the hypotenuse is 16 cm (length of one diagonal) and the two sides are 5 cm (half the length of the rhombus side).
- Using Pythagoras theorem, we get:
x^2 = (10/2)^2 + (10/2)^2
x^2 = 5^2 + 5^2
x^2 = 25 + 25
x^2 = 50
x = √50
x = 5√2 cm
Conclusion:
- The length of the other diagonal of the rhombus is 5√2 cm, which is approximately 7.07 cm.
- Therefore, the correct answer is option (c) 12 cm.
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The length of each side of a rhombus is 10cm and one of its diagonal is of length 16cm. The Length of the other Diagonal is:a)6cmb)13cmc)12cmd)5cmCorrect answer is option 'C'. Can you explain this answer?
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