Pythagorean Relationship

10 Grade 7 Mathematics questions on Pythagorean Relationship, with worked marking schemes. 10 questions are available on this topic in full.

1. Question 1

   1 mark

   Is a triangle with sides 5, 12, 13 a right triangle?

   A. Yes

   B. Only if equilateral

   C. Cannot tell

   D. No

   (1 mark)

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2. Question 2

   1 mark

   A rectangle is 8 cm by 6 cm. What is the diagonal?

   A. 10 cm

   B. 14 cm

   C. 7 cm

   D. 100 cm

   (1 mark)

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3. Question 3

   1 mark

   A ladder 3.2 m long leans at 30° to a wall. What is the distance from the foot of the wall?

   A. 2.8 m

   B. 3.2 m

   C. 1.6 m

   D. 6.4 m

   (1 mark)

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4. Question 4

   3 marks

   A ship sails 40 km north then 30 km east. How far is the ship from the starting point?

   (3 marks)

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5. Question 5

   2 marks

   A painter placed a 3.2 m long ladder at an angle of 30° with a vertical wall. What was the distance from the bottom of the ladder from the foot of the wall?

   A. 1.6 m

   B. 1.8 m

   C. 6.4 m

   D. 2.8 m

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6. Question 6

   2 marks

   The hypotenuse of a right triangle is 25 cm. One leg is 7 cm. Find the other leg.

   (2 marks)

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7. Question 7

   3 marks

   The diagonal of a square is 10 cm. Find the side of the square.

   (3 marks)

   Marking scheme

   A diagonal cuts the square into two right-angled triangles whose legs are both the side $s$, with the diagonal as hypotenuse. (1)

   By Pythagoras' theorem $s^2+s^2=10^2$, so $2s^2=100$ and $s^2=50$. (1)

   $s=\sqrt{50}=\sqrt{25\times 2}=5\sqrt{2}\approx 7.07$. (1)

   Final answer: $5\sqrt{2}$ cm, about $7.07$ cm.

8. Question 8

   3 marks

   A pole 12 m high is supported by a wire from the top to a point 5 m from the base. Find the length of the wire.

   (3 marks)

   Marking scheme

   The pole, the ground and the wire form a right-angled triangle, with the wire as the hypotenuse because it is opposite the right angle. (1)

   By Pythagoras' theorem the wire is $\sqrt{12^2+5^2}$ — add, because we are finding the hypotenuse. (1)

   $144+25=169$, and $\sqrt{169}=13$. (1)

   Final answer: $13$ m.

9. Question 9

   2 marks

   A painter placed a 3.2 m long ladder at an angle of 30° with a vertical wall. What was the distance from the bottom of the ladder from the foot of the wall?

   A. 1.6 m

   B. 1.8 m

   C. 6.4 m

   D. 2.8 m

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10. Question 10

    1 mark

    A right triangle has legs 3 cm and 4 cm. What is the hypotenuse?

    A. 6 cm

    B. 5 cm

    C. 7 cm

    D. 25 cm

    (1 mark)

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