MATHEMATICS - PYTHAGOREAN THEOREM

Pythagorean Theorem Practice Problems

10 questions
Know and use Pythagoras’ theorem.
Difficulty: Hard
Board: CAIE
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Q1.
A ladder of length $13\,\text{m}$ rests against a vertical wall. Its foot is initially $5\,\text{m}$ from the wall. The foot is then moved $3\,\text{m}$ farther from the wall. How far does the top of the ladder slide down the wall?

A) $4\,\text{m}$
B) $13-\sqrt{105}\,\text{m}$
C) $\sqrt{105}-8\,\text{m}$
D) $12-\sqrt{105}\,\text{m}$

Q2.
A rectangular garden has a diagonal of $26\,\text{m}$ and one side of length $10\,\text{m}$ . What length of fencing is needed to go once around the garden?

A) $72\,\text{m}$
B) $60\,\text{m}$
C) $68\,\text{m}$
D) $64\,\text{m}$

Q3.
An isosceles triangular roof section has two equal sides of $17\,\text{cm}$ and a base of $16\,\text{cm}$ . What is the area enclosed by the roof section?

A) $96\,\text{cm}^2$
B) $136\,\text{cm}^2$
C) $120\,\text{cm}^2$
D) $128\,\text{cm}^2$

Q4.
Two vertical poles stand on level ground with their bases $35\,\text{m}$ apart. Their heights are $8\,\text{m}$ and $20\,\text{m}$ . A cable joins their tops and includes an extra $2\,\text{m}$ for fastening. What cable length is required?

A) $41\,\text{m}$
B) $37\,\text{m}$
C) $39\,\text{m}$
D) $49\,\text{m}$

Q5.
A taut kite string is $50\,\text{m}$ long. The kite is horizontally $14\,\text{m}$ from the point directly below the person's hand. The hand is $1.5\,\text{m}$ above level ground. How high is the kite above the ground?

A) $49.5\,\text{m}$
B) $48\,\text{m}$
C) $51.5\,\text{m}$
D) $47.5\,\text{m}$

Q6.
The diagonal of a square courtyard is $\sqrt{288}\,\text{m}$ . What is the area of the courtyard?

A) $576\,\text{m}^2$
B) $288\,\text{m}^2$
C) $72\,\text{m}^2$
D) $144\,\text{m}^2$

Q7.
A rhombus has side length $13\,\text{cm}$ . One of its diagonals is $10\,\text{cm}$ . The diagonals bisect each other at right angles. What is the area of the rhombus?

A) $120\,\text{cm}^2$
B) $130\,\text{cm}^2$
C) $60\,\text{cm}^2$
D) $100\,\text{cm}^2$

Q8.
Use the measurements and right-angle marks in the figure to find the perimeter of quadrilateral $ABCD$ .

Diagram for question 8: Use the measurements and right-angle marks in the figure to find the perimeter of quadrilateral ABCD.

A) $42\,\text{cm}$
B) $44\,\text{cm}$
C) $54\,\text{cm}$
D) $46\,\text{cm}$

Q9.
The figure shows a vertical mast supported by two straight wires. What is the combined length of the two wires?

Diagram for question 9: The figure shows a vertical mast supported by two straight wires. What is the combined length of the two…

A) $40\,\text{m}$
B) $37\,\text{m}$
C) $32\,\text{m}$
D) $35\,\text{m}$

Q10.
Use the dimensions in the figure to calculate the perimeter of trapezium $ABCD$ .

Diagram for question 10: Use the dimensions in the figure to calculate the perimeter of trapezium ABCD.

A) $43+\sqrt{41}\,\text{cm}$
B) $58\,\text{cm}$
C) $43+3\sqrt{41}\,\text{cm}$
D) $31+3\sqrt{41}\,\text{cm}$

What this assessment covers

Concepts Tested

pythagorean theorem
Know and use Pythagoras’ theorem.

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Assessment details

Total questions:: 10
Subject:: Mathematics
Topic:: Pythagorean Theorem
Difficulty:: Hard
Grade:: Grade 6
Board:: CAIE
Marks:: 10.00

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Q1. A ladder of length 13 m rests against a vertical wall. Its foot is initially 5 m from the wall. The foot is then moved 3 m farther from the wall. How far does the top of the ladder slide down the wall?

Q2. A rectangular garden has a diagonal of 26 m and one side of length 10 m. What length of fencing is needed to go once around the garden?

Q3. An isosceles triangular roof section has two equal sides of 17 cm and a base of 16 cm. What is the area enclosed by the roof section?

Q4. Two vertical poles stand on level ground with their bases 35 m apart. Their heights are 8 m and 20 m. A cable joins their tops and includes an extra 2 m for fastening. What cable length is required?

Q5. A taut kite string is 50 m long. The kite is horizontally 14 m from the point directly below the person's hand. The hand is 1.5 m above level ground. How high is the kite above the ground?

Q6. The diagonal of a square courtyard is √(288) m. What is the area of the courtyard?

Q7. A rhombus has side length 13 cm. One of its diagonals is 10 cm. The diagonals bisect each other at right angles. What is the area of the rhombus?

Q8. Use the measurements and right-angle marks in the figure to find the perimeter of quadrilateral ABCD.

Q9. The figure shows a vertical mast supported by two straight wires. What is the combined length of the two wires?

Q10. Use the dimensions in the figure to calculate the perimeter of trapezium ABCD.