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The length of diagonals of a rhombus are 30 cm and 40 cm. Find the side of rhombus?
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The length of diagonals of a rhombus are 30 cm and 40 cm. Find the sid...
Given:
- The length of diagonals of a rhombus are 30 cm and 40 cm.
To find:
- The side of the rhombus.
Solution:
- A rhombus is a quadrilateral with all sides equal in length.
- The diagonals of a rhombus bisect each other at right angles.
- In a rhombus, the diagonals are perpendicular bisectors of each other.
- Let AC and BD be the diagonals of the rhombus.
- Given, AC = 30 cm and BD = 40 cm.
- Let AB = BC = CD = DA = x (Let x be the side of the rhombus)
- As the diagonals of the rhombus bisect each other at right angles, we can apply the Pythagorean theorem to find x.
- From the above figure, we can see that:
- AC and BD are the diagonals of the rhombus.
- AE = CE and BE = DE (as diagonals bisect each other)
- Therefore, AD = DC = BC = AB = x/2 (as diagonals bisect each other)
- Applying the Pythagorean theorem in right-angled triangles AED and BEC, we get:
- AE² + ED² = AD²
- BE² + EC² = BC²
- Substituting the values, we get:
- (x/2)² + (x/2)² = (30/2)²
- (x/2)² + (x/2)² = 225
- 2(x/2)² = 225
- x²/2 = 225
- x² = 450
- x = √450
- x = 15√2
- Therefore, the side of the rhombus is 15√2 cm.
Community Answer
The length of diagonals of a rhombus are 30 cm and 40 cm. Find the sid...
D1 = 30 cm D1/2 = 15 cm
D2 = 40 cm D2/2 = 20 cm
by pythagoras theorem
side of rhombus = rt under [15]*2 + [20]*2
root under 225 + 400
root under 625
25 cm
All sides of rhombus are equal
Therefore side of rhombus = 25 cm
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The length of diagonals of a rhombus are 30 cm and 40 cm. Find the side of rhombus?
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The length of diagonals of a rhombus are 30 cm and 40 cm. Find the side of rhombus? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The length of diagonals of a rhombus are 30 cm and 40 cm. Find the side of rhombus? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of diagonals of a rhombus are 30 cm and 40 cm. Find the side of rhombus?.
The length of diagonals of a rhombus are 30 cm and 40 cm. Find the side of rhombus? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The length of diagonals of a rhombus are 30 cm and 40 cm. Find the side of rhombus? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of diagonals of a rhombus are 30 cm and 40 cm. Find the side of rhombus?.
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