Class 8 Pythagoras Theorem — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. In a right-angled triangle, what is the side opposite the right angle called?
AThe median
BThe base
CThe hypotenuse
DThe height
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Answer: C) The hypotenuse
The side opposite the right angle is the hypotenuse. It is always the longest side.
2. The legs of a right triangle are 7 cm and 24 cm. How long is the hypotenuse?
A31 cm
B26 cm
C25 cm
D17 cm
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Answer: C) 25 cm
72+242=49+576=625, and 625=25 cm.
3. The diagonals of a rhombus are 16 cm and 12 cm. Find the length of a side.
A20 cm
B10 cm
C28 cm
D14 cm
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Answer: B) 10 cm
Diagonals of a rhombus bisect each other at right angles, giving half-diagonals 8 cm and 6 cm. Side² = 64 + 36 = 100, so side = 10 cm. Using the full diagonals gives the wrong 20 cm.
4. Sunil says a right triangle with legs 5 cm and 7 cm has hypotenuse 12 cm. What is the correct hypotenuse?
AAbout 8.6 cm
B74 cm
C12 cm
DAbout 4.9 cm
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Answer: A) About 8.6 cm
Sunil added the legs. Correct: 25+49=74≈8.6 cm. A hypotenuse is always shorter than the two legs together.
5. Using (2mn,m2−n2,m2+n2) with m = 4 and n = 1 gives which triple?