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If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find the area of the rhombus.
- a)54 sq. cm.
- b)108 sq. cm.
- c)144 sq. cm.
- d)200 sq. cm.
- e)None of the above
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find...
It is given that the length of the diagonals are in 3:4. Let '3x', and '4x' be the lengths of semi-diagonals as shown in the figure. We know that diagonals of a rhombus intersect each other perpendicularly.
In right angle triangle AOB,
AB2 = AO2 + BO2
=>15 = 5x
=>x = 3cm.
Therefore, we can say that the length of diagonals = 6x and 8x or 18 and 24 cm.
Hence, the area of the rhombus = 1/2 * 18 * 24 = 216 cm2. Therefore, option E is the correct answer.
Most Upvoted Answer
If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find...
Given:
- The side of the rhombus is 15 cm.
- The diagonals of the rhombus are in the ratio 3:4.
To find:
- The area of the rhombus.
Solution:
Let the diagonals of the rhombus be 3x and 4x.
Using Pythagoras theorem, we can find the length of each side of the rhombus.
Length of each side of the rhombus = (1/2) * √(3x)^2 + (4x)^2
= (1/2) * √(9x^2 + 16x^2)
= (1/2) * √(25x^2)
= (1/2) * 5x
= 2.5x
Since the diagonals of a rhombus are perpendicular bisectors of each other, we can use the length of the diagonals to find x:
3x + 4x = 2 * diagonal
7x = 2 * diagonal
x = (2/7) * diagonal
Substituting the value of x in the length of each side of the rhombus:
Length of each side of the rhombus = 2.5x
= 2.5 * (2/7) * diagonal
= (5/7) * diagonal
Since the length of each side of the rhombus is 15 cm:
(5/7) * diagonal = 15
Diagonal = (7/5) * 15
= 21
Using the length of the diagonals, we can find the area of the rhombus:
Area of the rhombus = (1/2) * product of diagonals
= (1/2) * 3x * 4x
= (1/2) * 3 * 4 * (21/7)^2
= 54 sq. cm (approx)
Therefore, the correct answer is (a) 54 sq. cm.
- The side of the rhombus is 15 cm.
- The diagonals of the rhombus are in the ratio 3:4.
To find:
- The area of the rhombus.
Solution:
Let the diagonals of the rhombus be 3x and 4x.
Using Pythagoras theorem, we can find the length of each side of the rhombus.
Length of each side of the rhombus = (1/2) * √(3x)^2 + (4x)^2
= (1/2) * √(9x^2 + 16x^2)
= (1/2) * √(25x^2)
= (1/2) * 5x
= 2.5x
Since the diagonals of a rhombus are perpendicular bisectors of each other, we can use the length of the diagonals to find x:
3x + 4x = 2 * diagonal
7x = 2 * diagonal
x = (2/7) * diagonal
Substituting the value of x in the length of each side of the rhombus:
Length of each side of the rhombus = 2.5x
= 2.5 * (2/7) * diagonal
= (5/7) * diagonal
Since the length of each side of the rhombus is 15 cm:
(5/7) * diagonal = 15
Diagonal = (7/5) * 15
= 21
Using the length of the diagonals, we can find the area of the rhombus:
Area of the rhombus = (1/2) * product of diagonals
= (1/2) * 3x * 4x
= (1/2) * 3 * 4 * (21/7)^2
= 54 sq. cm (approx)
Therefore, the correct answer is (a) 54 sq. cm.
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Community Answer
If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find...
It is given that the length of the diagonals are in 3:4. Let '3x', and '4x' be the lengths of semi-diagonals as shown in the figure. We know that diagonals of a rhombus intersect each other perpendicularly.
In right angle triangle AOB,
AB2 = AO2 + BO2
=>15 = 5x
=>x = 3cm.
Therefore, we can say that the length of diagonals = 6x and 8x or 18 and 24 cm.
Hence, the area of the rhombus = 1/2 * 18 * 24 = 216 cm2. Therefore, option E is the correct answer.
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If the diagonals of a rhombus of side 15 cm are in the ratio 3:4, find the area of the rhombus.a)54 sq. cm.b)108 sq. cm.c)144 sq. cm.d)200 sq. cm.e)None of the aboveCorrect answer is option 'E'. Can you explain this answer?
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