Class 9 Exam > Class 9 Questions > In triangle PQR length of the side QR is less...
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In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :
- a)6 cm
- b)8 cm
- c)7 cm
- d)10 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In triangle PQR length of the side QR is less than twice the length of...
Given:
- QR < 2pq="" -="" />
- PR = PQ + 10
- PQ + QR + PR = 40
To find:
The length of the smallest side of the triangle PQR.
Solution:
1. Simplify the first equation:
QR < 2pq="" -="" 2="" />
QR + 2 < 2pq="" />
PQ > (QR + 2)/2
2. Substitute PR and PQ in terms of QR in the third equation:
PQ + QR + PR = 40
((QR + 2)/2) + QR + ((QR + 2)/2 + 10) = 40
3QR + 14 = 40
3QR = 26
QR = 8.67
3. Substitute QR into the first equation to find PQ:
PQ > (QR + 2)/2
PQ > (8.67 + 2)/2
PQ > 5.34
4. Substitute PQ and QR into the second equation to find PR:
PR = PQ + 10
PR = 5.34 + 10
PR = 15.34
5. Check that the sum of all sides is 40:
PQ + QR + PR = 5.34 + 8.67 + 15.34 = 29.35
6. Since PQ is the smallest side, the answer is 8 cm (rounded to the nearest whole number).
Therefore, the length of the smallest side of the triangle PQR is 8 cm.
- QR < 2pq="" -="" />
- PR = PQ + 10
- PQ + QR + PR = 40
To find:
The length of the smallest side of the triangle PQR.
Solution:
1. Simplify the first equation:
QR < 2pq="" -="" 2="" />
QR + 2 < 2pq="" />
PQ > (QR + 2)/2
2. Substitute PR and PQ in terms of QR in the third equation:
PQ + QR + PR = 40
((QR + 2)/2) + QR + ((QR + 2)/2 + 10) = 40
3QR + 14 = 40
3QR = 26
QR = 8.67
3. Substitute QR into the first equation to find PQ:
PQ > (QR + 2)/2
PQ > (8.67 + 2)/2
PQ > 5.34
4. Substitute PQ and QR into the second equation to find PR:
PR = PQ + 10
PR = 5.34 + 10
PR = 15.34
5. Check that the sum of all sides is 40:
PQ + QR + PR = 5.34 + 8.67 + 15.34 = 29.35
6. Since PQ is the smallest side, the answer is 8 cm (rounded to the nearest whole number).
Therefore, the length of the smallest side of the triangle PQR is 8 cm.
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Community Answer
In triangle PQR length of the side QR is less than twice the length of...
Let's pq = x,
so,qr=2x-2 and pr=x+10
A/Q,
x+2x-2+x+10=40
4x+8=40
4x=40-8
4x=32
x=32÷4
x=8
so,qr=2x-2 and pr=x+10
A/Q,
x+2x-2+x+10=40
4x+8=40
4x=40-8
4x=32
x=32÷4
x=8
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In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer?.
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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Here you can find the meaning of In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :a)6 cmb)8 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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