1. In a right-angled triangle, the side opposite the right angle is called the:
- AHypotenuse
- BBase
- CAltitude
- DMedian
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Answer: A) Hypotenuse
The side opposite the right angle is the longest side and is called the hypotenuse.
Class 7 Pythagoras Property — practice questions with answers
Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. A right triangle has hypotenuse 25 cm and one leg 7 cm. Find the other leg.
- A48
- B24
- C22
- D26
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Answer: B) 24
leg² = 25² - 7² = 625 - 49 = 576, so leg = = 24 cm.
3. In a right triangle, if hypotenuse = 15 cm and one leg = 9 cm, the other leg is:
- A12 cm
- B13 cm
- C6 cm
- D24 cm
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Answer: A) 12 cm
leg² = 15² - 9² = 225 - 81 = 144, so leg = 12 cm.
4. The sides of a triangle are 11 cm, 60 cm and 61 cm.
Using the converse of the Pythagoras property, what type of triangle is it?
Using the converse of the Pythagoras property, what type of triangle is it?
- ARight-angled
- BAcute-angled
- CObtuse-angled
- DNot a valid triangle
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Answer: A) Right-angled
11² + 60² = 121 + 3600 = 3721 = 61², so it is right-angled.
5. A right triangle has legs in the ratio 3 : 4 and a hypotenuse of 30 cm.
Find the length of the shorter leg.
Find the length of the shorter leg.
- A19
- B18
- C17
- D36
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Answer: B) 18
Let legs be 3k and 4k. Then (3k)² + (4k)² = 30², so 9k² + 16k² = 900, 25 k² = 900, k² = 36, k = 6. Shorter leg = 3k = 18 cm.
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