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The length of one side of a rhombus is 17 cm and one of the diagonals was 16 cm. Find the length of the other diagonal.
- a)16 cm
- b)20 cm
- c)32 cm
- d)30 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The length of one side of a rhombus is 17 cm and one of the diagonals ...
Given, side of the rhombus = 17 cm and one diagonal (d1) = 16 cm
Let another diagonal (d2) = x cm
Since, Diagonals of the rhombus bisect each other at right angle
From Pythagoras theorem,
(side)2 = (d1/2)2 + (d2/2)2
⇒ 172 = (16/2)2 + (x/2)2
⇒ 289 = 64 + x2/4
⇒ x2/4 = 225
⇒ x2 = 225 × 4
⇒ x = 15 × 2
∴ x = 30 cm
Since, Diagonals of the rhombus bisect each other at right angle
From Pythagoras theorem,
(side)2 = (d1/2)2 + (d2/2)2
⇒ 172 = (16/2)2 + (x/2)2
⇒ 289 = 64 + x2/4
⇒ x2/4 = 225
⇒ x2 = 225 × 4
⇒ x = 15 × 2
∴ x = 30 cm
Most Upvoted Answer
The length of one side of a rhombus is 17 cm and one of the diagonals ...
To find the length of the other diagonal of a rhombus, we can use the Pythagorean theorem and the properties of a rhombus.
Given:
Length of one side of the rhombus = 17 cm
Length of one diagonal = 16 cm
Step 1: Understanding the properties of a rhombus
A rhombus is a quadrilateral with all four sides of equal length. The diagonals of a rhombus bisect each other at right angles.
Step 2: Finding the length of the other diagonal using the Pythagorean theorem
In a rhombus, the diagonals divide the rhombus into four congruent right-angled triangles. Let's consider one of these triangles.
The length of one side of the rhombus = 17 cm
The length of one diagonal = 16 cm
Using the Pythagorean theorem, we can find the length of the other side of the rhombus:
(side of the rhombus)^2 = (one-half of the diagonal)^2 + (one-half of the diagonal)^2
(17/2)^2 = (16/2)^2 + (length of the other side)^2
(8.5)^2 = (8)^2 + (length of the other side)^2
(8.5)^2 - (8)^2 = (length of the other side)^2
(72.25 - 64) = (length of the other side)^2
8.25 = (length of the other side)^2
Taking the square root of both sides, we get:
length of the other side = √8.25
Step 3: Finding the length of the other diagonal
Since the diagonals of a rhombus bisect each other at right angles, the length of the other diagonal is twice the length of the other side of the rhombus.
length of the other diagonal = 2 * length of the other side
length of the other diagonal = 2 * √8.25
length of the other diagonal ≈ 2 * 2.872
length of the other diagonal ≈ 5.744
Rounding to the nearest whole number, we get:
length of the other diagonal ≈ 6 cm
Therefore, the length of the other diagonal is approximately 6 cm, which is not among the answer options provided. It appears there may be an error in the given options.
Given:
Length of one side of the rhombus = 17 cm
Length of one diagonal = 16 cm
Step 1: Understanding the properties of a rhombus
A rhombus is a quadrilateral with all four sides of equal length. The diagonals of a rhombus bisect each other at right angles.
Step 2: Finding the length of the other diagonal using the Pythagorean theorem
In a rhombus, the diagonals divide the rhombus into four congruent right-angled triangles. Let's consider one of these triangles.
The length of one side of the rhombus = 17 cm
The length of one diagonal = 16 cm
Using the Pythagorean theorem, we can find the length of the other side of the rhombus:
(side of the rhombus)^2 = (one-half of the diagonal)^2 + (one-half of the diagonal)^2
(17/2)^2 = (16/2)^2 + (length of the other side)^2
(8.5)^2 = (8)^2 + (length of the other side)^2
(8.5)^2 - (8)^2 = (length of the other side)^2
(72.25 - 64) = (length of the other side)^2
8.25 = (length of the other side)^2
Taking the square root of both sides, we get:
length of the other side = √8.25
Step 3: Finding the length of the other diagonal
Since the diagonals of a rhombus bisect each other at right angles, the length of the other diagonal is twice the length of the other side of the rhombus.
length of the other diagonal = 2 * length of the other side
length of the other diagonal = 2 * √8.25
length of the other diagonal ≈ 2 * 2.872
length of the other diagonal ≈ 5.744
Rounding to the nearest whole number, we get:
length of the other diagonal ≈ 6 cm
Therefore, the length of the other diagonal is approximately 6 cm, which is not among the answer options provided. It appears there may be an error in the given options.
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Community Answer
The length of one side of a rhombus is 17 cm and one of the diagonals ...
Given, side of the rhombus = 17 cm and one diagonal (d1) = 16 cm
Let another diagonal (d2) = x cm
Since, Diagonals of the rhombus bisect each other at right angle
From Pythagoras theorem,
(side)2 = (d1/2)2 + (d2/2)2
⇒ 172 = (16/2)2 + (x/2)2
⇒ 289 = 64 + x2/4
⇒ x2/4 = 225
⇒ x2 = 225 × 4
⇒ x = 15 × 2
∴ x = 30 cm
Since, Diagonals of the rhombus bisect each other at right angle
From Pythagoras theorem,
(side)2 = (d1/2)2 + (d2/2)2
⇒ 172 = (16/2)2 + (x/2)2
⇒ 289 = 64 + x2/4
⇒ x2/4 = 225
⇒ x2 = 225 × 4
⇒ x = 15 × 2
∴ x = 30 cm
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The length of one side of a rhombus is 17 cm and one of the diagonals was 16 cm. Find the length of the other diagonal.a)16 cmb)20 cmc)32 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer?
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