Class 10 Pythagoras Theorem — practice questions with answers

Geometry — Similarity · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. In a right triangle the two legs are 3 cm and 4 cm. What is the length of the hypotenuse?

A5 cm
B6 cm
C7 cm
D12 cm

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Answer: A) 5 cm

Hypotenuse =

3^{2} + 4^{2}

9 + 16

25

= 5 cm.

2. In an isosceles right triangle each equal leg is 1 unit. The hypotenuse is:

A $2$
B2
C1
D $3$

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Answer: A)

2

Hypotenuse =

1^{2} + 1^{2}

2

3. If the hypotenuse of a right triangle is 17 cm and one leg is 15 cm, the third side is:

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Answer: B) 8

1 7^{2} - 1 5^{2}

289 - 225

64

= 8 cm.

4. A right triangle has its two legs as consecutive even integers.
The hypotenuse is 10 cm.
Find the smaller leg (in cm).

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Answer: C) 6

Let legs be 2n and 2n+2. (2n)² + (2n+2)² = 100. 4n² + 4n² + 8n + 4 = 100. 8n² + 8n - 96 = 0, n² + n - 12 = 0, (n+4)(n-3)=0, n=3. Smaller leg = 2n = 6 cm (legs 6 and 8).

5. ABCD is a square of side 10 cm. P is the midpoint of side BC and Q is the midpoint of side CD.
Using the right angle at C, find the length of PQ, in cm (give to two decimals).

A14.14
B8.07
C7.07
D6.07

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Answer: C) 7.07

CP = CQ = 5 cm and angle PCQ = 90 deg. PQ =

5^{2} + 5^{2}

50

52

approx 7.07 cm.

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