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The ratio of two unequal sides of a rectangle is 1:2. If its perimeter is 24cm, then length of diagonal is
  • a)
    8/√5 cm
  • b)
    4√5 cm
  • c)
    4/√5 cm
  • d)
    2√5 cm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The ratio of two unequal sides of a rectangle is 1:2. If its perimeter...
Let the sides of rectangle are x and 2x respectively. Then
2(x + 2x) = 24
⇒ x = 4
∴ Sides are 4 and 8 respectively.
Then length of diagonal 
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Most Upvoted Answer
The ratio of two unequal sides of a rectangle is 1:2. If its perimeter...
Understanding the Problem
To determine the length of the diagonal of a rectangle with a perimeter of 24 cm and a side ratio of 1:2, we begin by defining the sides.
Defining the Sides
- Let the shorter side be x.
- The longer side, according to the ratio 1:2, will be 2x.
Calculating the Perimeter
The formula for the perimeter (P) of a rectangle is given by:
P = 2(length + width)
- Substituting the values:
2(x + 2x) = 24
- Simplifying:
2(3x) = 24
6x = 24
x = 4 cm
Determining the Dimensions
- Shorter side = x = 4 cm
- Longer side = 2x = 8 cm
Calculating the Diagonal
The diagonal (d) of a rectangle can be found using the Pythagorean theorem:
d = √(length² + width²)
- Substituting the values:
d = √(4² + 8²)
d = √(16 + 64)
d = √80
d = √(16 × 5)
d = 4√5 cm
Conclusion
The length of the diagonal of the rectangle is 4√5 cm. Thus, the correct answer is option B.
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The ratio of two unequal sides of a rectangle is 1:2. If its perimeter is 24cm, then length of diagonal isa)8/√5 cmb)4√5 cmc)4/√5 cmd)2√5 cmCorrect answer is option 'B'. Can you explain this answer?
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