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In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if ac is 21cm, bc is 29cm, ab is 30cm. find the perimeter of quadrilateral arpq?
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In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if...
To find the perimeter of quadrilateral ARPQ in triangle ABC, where P, Q, and R are the midpoints of sides BC, CA, and AB respectively, we can follow these steps:
1. Understand the Triangle and Midpoints
- Given sides:
- AC = 21 cm
- BC = 29 cm
- AB = 30 cm
- Midpoints:
- P = Midpoint of BC
- Q = Midpoint of CA
- R = Midpoint of AB
2. Calculate the Lengths of AR, RP, PQ, and QA
- Since P, Q, and R are midpoints, we can use the property that the segment connecting midpoints of two sides of a triangle is half the length of the third side.
- Lengths of the segments:
- AR = 1/2 * BC = 1/2 * 29 cm = 14.5 cm
- RP = 1/2 * AC = 1/2 * 21 cm = 10.5 cm
- PQ = 1/2 * AB = 1/2 * 30 cm = 15 cm
3. Calculate the Perimeter of Quadrilateral ARPQ
- The perimeter (P) of quadrilateral ARPQ can be calculated by adding the lengths of its sides:
P = AR + RP + PQ + QA
- Since Q is the midpoint of AC, QA = 1/2 * AB = 15 cm.
- Thus, the perimeter calculation is:
P = 14.5 cm + 10.5 cm + 15 cm + 15 cm
4. Final Calculation
- Adding these values:
P = 14.5 + 10.5 + 15 + 15 = 55 cm
Conclusion
- The perimeter of quadrilateral ARPQ is 55 cm.
1. Understand the Triangle and Midpoints
- Given sides:
- AC = 21 cm
- BC = 29 cm
- AB = 30 cm
- Midpoints:
- P = Midpoint of BC
- Q = Midpoint of CA
- R = Midpoint of AB
2. Calculate the Lengths of AR, RP, PQ, and QA
- Since P, Q, and R are midpoints, we can use the property that the segment connecting midpoints of two sides of a triangle is half the length of the third side.
- Lengths of the segments:
- AR = 1/2 * BC = 1/2 * 29 cm = 14.5 cm
- RP = 1/2 * AC = 1/2 * 21 cm = 10.5 cm
- PQ = 1/2 * AB = 1/2 * 30 cm = 15 cm
3. Calculate the Perimeter of Quadrilateral ARPQ
- The perimeter (P) of quadrilateral ARPQ can be calculated by adding the lengths of its sides:
P = AR + RP + PQ + QA
- Since Q is the midpoint of AC, QA = 1/2 * AB = 15 cm.
- Thus, the perimeter calculation is:
P = 14.5 cm + 10.5 cm + 15 cm + 15 cm
4. Final Calculation
- Adding these values:
P = 14.5 + 10.5 + 15 + 15 = 55 cm
Conclusion
- The perimeter of quadrilateral ARPQ is 55 cm.
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In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if ac is 21cm, bc is 29cm, ab is 30cm. find the perimeter of quadrilateral arpq?
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In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if ac is 21cm, bc is 29cm, ab is 30cm. find the perimeter of quadrilateral arpq? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if ac is 21cm, bc is 29cm, ab is 30cm. find the perimeter of quadrilateral arpq? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if ac is 21cm, bc is 29cm, ab is 30cm. find the perimeter of quadrilateral arpq?.
In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if ac is 21cm, bc is 29cm, ab is 30cm. find the perimeter of quadrilateral arpq? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if ac is 21cm, bc is 29cm, ab is 30cm. find the perimeter of quadrilateral arpq? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle abc pq and r are the midpoints of sides bc,ca and ab. if ac is 21cm, bc is 29cm, ab is 30cm. find the perimeter of quadrilateral arpq?.
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