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If the sides of a rectangle are increased by 10% find the percentage increased in its diagonals.
- a)20%
- b)10%
- c)15%
- d)18%
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the sides of a rectangle are increased by 10% find the percentage i...
According to the formula,
∵ Percentage increase in sides = 10%
∴ Percentage increase diagonals = 10%
∵ Percentage increase in sides = 10%
∴ Percentage increase diagonals = 10%
Most Upvoted Answer
If the sides of a rectangle are increased by 10% find the percentage i...
Explanation:
Increasing the sides of a rectangle by 10% will result in increasing both the length and width by 10%.
Increasing the length and width of the rectangle by 10% can be calculated as follows:
Let the original length = L and original width = W
New length = L + 0.10L = 1.10L
New width = W + 0.10W = 1.10W
Calculating the Diagonal:
The diagonal of a rectangle can be calculated using the Pythagorean theorem:
Diagonal = √(Length^2 + Width^2)
Calculating the Original Diagonal:
Original Diagonal = √(L^2 + W^2)
Calculating the New Diagonal:
New Diagonal = √((1.10L)^2 + (1.10W)^2)
New Diagonal = √(1.21L^2 + 1.21W^2)
New Diagonal = 1.1√(L^2 + W^2)
Calculating the Percentage Increase:
Percentage Increase = ((New Diagonal - Original Diagonal) / Original Diagonal) * 100
Percentage Increase = ((1.1√(L^2 + W^2) - √(L^2 + W^2)) / √(L^2 + W^2)) * 100
Percentage Increase = (0.1 / 1) * 100
Percentage Increase = 10%
Therefore, the percentage increase in the diagonals of the rectangle when the sides are increased by 10% is 10%. Hence, the correct answer is option 'B'.
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