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The ratio of two unequal sides of a rectangle is 1 : 2. If its perimeter is 24 cm, then the length of diagonal in cm is:
  • a)
    2/√5
  • b)
    4/√5
  • c)
    2√5
  • d)
    4√5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The ratio of two unequal sides of a rectangle is 1 : 2. If its perime...
Let the sides of rectangle be 2x, x cm
∴ Perimeter of rectangle = 2 (2x+x)
2 (2x+x) = 24
or 6x = 24
∴ x = 4 cm
hence length of diagonal = √[(2x)2+x2]
= √5x2
= √(5×16)
=√ 80
= 4√5
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Most Upvoted Answer
The ratio of two unequal sides of a rectangle is 1 : 2. If its perime...
Given information:
- Ratio of two unequal sides of the rectangle: 1 : 2
- Perimeter of the rectangle: 24 cm

Calculating the sides of the rectangle:
Let the sides of the rectangle be 1x and 2x (based on the given ratio).
Perimeter of a rectangle = 2(length + width)
24 = 2(1x + 2x)
24 = 2(3x)
24 = 6x
x = 4
Therefore, the sides of the rectangle are 4 cm and 8 cm.

Calculating the diagonal of the rectangle:
In a rectangle, the diagonal can be calculated using the Pythagorean theorem.
Diagonal = √(length^2 + width^2)
Diagonal = √(4^2 + 8^2)
Diagonal = √(16 + 64)
Diagonal = √80
Diagonal = 4√5 cm
Therefore, the length of the diagonal of the rectangle is 4√5 cm, which matches with option 'D'.
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The ratio of two unequal sides of a rectangle is 1 : 2. If its perimeter is 24 cm, then the length of diagonal in cm is:a)2/√5b)4/√5c)2√5d)4√5Correct answer is option 'D'. Can you explain this answer?
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