Short Questions
Q1. Find the diagonal of a square of side 6 cm.
Solution:
We know: diagonal = side × √2
= 6√2 cm
Answer: 6√2 cm
Q2. Find the hypotenuse of an isosceles right triangle with equal sides 5 cm.
Solution:
c² = 2 × 5² = 2 × 25 = 50
c = √50 = 5√2
Answer: 5√2 cm
Q3. Check whether (6, 8, 10) is a Baudhāyana triple.
Solution:
6² + 8² = 36 + 64 = 100
10² = 100
Since both are equal → Yes
Answer: Yes, it is a triple
Q4. Find the missing side if a = 9 cm, b = 12 cm.
Solution:
c² = 9² + 12² = 81 + 144 = 225
c = 15
Answer: 15 cm
Q5. Find the area of square whose diagonal is √8 cm.
Solution:
Side = √(diagonal² ÷ 2)
= √(8 ÷ 2) = √4 = 2
Area = 2² = 4
Answer: 4 sq cm
Q6. Find the hypotenuse when sides are 5 cm and 12 cm.
Solution:
c² = 25 + 144 = 169
c = 13
Answer: 13 cm
Q7. Is (9, 12, 15) a primitive triple?
Solution:
All numbers divisible by 3 → not primitive
Answer: No
Q8. Find the value of √2 correct up to 2 decimal places.
Solution:
√2 ≈ 1.414
Answer: 1.41
Q9. Find the hypotenuse if both sides are 10 cm.
Solution:
c² = 2 × 10² = 200
c = √200 = 10√2
Answer: 10√2 cm
Q10. Find the third side if hypotenuse = 17 cm and one side = 8 cm.
Solution:
b² = 17² − 8² = 289 − 64 = 225
b = 15
Answer: 15 cm
Long Questions
Q1. Find the hypotenuse of a right triangle with sides 7 cm and 24 cm.
Solution:
c² = 7² + 24²
= 49 + 576 = 625
c = √625 = 25
Answer: 25 cm
Q2. Find the length of equal sides of an isosceles right triangle if hypotenuse is √72.
Solution:
72 = 2a²
a² = 36
a = 6
Answer: 6 cm each
Q3. Find the diagonal of a square of side 8 cm and its area.
Solution:
Diagonal = 8√2
Area = 8² = 64
Answer:
Diagonal = 8√2 cm
Area = 64 sq cm
Q4. A right triangle has sides 15 cm and 20 cm. Find its hypotenuse and verify the theorem.
Solution:
c² = 15² + 20²
= 225 + 400 = 625
c = 25
Verification:
15² + 20² = 25² ✔
Answer: 25 cm
Q5. Find the missing side of a triangle where a = 9 cm and hypotenuse = 15 cm.
Solution:
b² = 15² − 9²
= 225 − 81 = 144
b = 12
Answer: 12 cm
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