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ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.
- a)8 cm
- b)5 cm
- c)7 cm
- d)3 cm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm...
Using pythagoras theorem,
QR2 = PR2 + PQ2
42+32
=16+9=25
QR = 5cm
QR2 = PR2 + PQ2
42+32
=16+9=25
QR = 5cm
Most Upvoted Answer
ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm...
Using pythagoras theorem,
QR2 = PR2 + PQ2
42+32
=16+9=25
QR = 5cm
QR2 = PR2 + PQ2
42+32
=16+9=25
QR = 5cm
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Community Answer
ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm...
Understanding the Triangle
In triangle PQR, we know it is right-angled at point P. This means we can apply the Pythagorean theorem to find the length of side QR.
Given Measurements
- PQ = 3 cm (one leg of the triangle)
- PR = 4 cm (the other leg of the triangle)
Pythagorean Theorem
The Pythagorean theorem states that in a right triangle:
QR² = PQ² + PR²
Where QR is the hypotenuse.
Calculating QR
Let's substitute the known values into the formula:
- First, square the lengths of PQ and PR:
- PQ² = 3² = 9
- PR² = 4² = 16
- Now, add these squares together:
- QR² = 9 + 16 = 25
- Finally, take the square root to find QR:
- QR = √25 = 5 cm
Conclusion
The length of side QR is 5 cm. Therefore, the correct answer is option 'B'.
This method effectively uses the properties of right triangles to determine the length of the hypotenuse, providing a clear solution to the problem.
In triangle PQR, we know it is right-angled at point P. This means we can apply the Pythagorean theorem to find the length of side QR.
Given Measurements
- PQ = 3 cm (one leg of the triangle)
- PR = 4 cm (the other leg of the triangle)
Pythagorean Theorem
The Pythagorean theorem states that in a right triangle:
QR² = PQ² + PR²
Where QR is the hypotenuse.
Calculating QR
Let's substitute the known values into the formula:
- First, square the lengths of PQ and PR:
- PQ² = 3² = 9
- PR² = 4² = 16
- Now, add these squares together:
- QR² = 9 + 16 = 25
- Finally, take the square root to find QR:
- QR = √25 = 5 cm
Conclusion
The length of side QR is 5 cm. Therefore, the correct answer is option 'B'.
This method effectively uses the properties of right triangles to determine the length of the hypotenuse, providing a clear solution to the problem.
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ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.a)8 cmb)5 cmc)7 cmd)3 cmCorrect answer is option 'B'. Can you explain this answer?
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