Open Math
Pythagoras' theorem
Measurement · MA4-PYT-C-01
Finding the hypotenuse
Q1Straightforward
A right-angled triangle has legs of length 3 cm and 4 cm. Find the length of the hypotenuse. Q2Straightforward
A right-angled triangle has legs of length 5 cm and 12 cm. Find the length of the hypotenuse. Q3Straightforward
A right-angled triangle has legs of length 6 cm and 8 cm. Find the length of the hypotenuse. Q4Straightforward
A right-angled triangle has legs of length 8 cm and 15 cm. Find the length of the hypotenuse. Q5Moderate
A right-angled triangle has legs of length 3 cm and 5 cm. Find the length of the hypotenuse, rounded to 2 decimal places. Q6Moderate
A right-angled triangle has legs of length 4 cm and 7 cm. Find the length of the hypotenuse, rounded to 2 decimal places. Q7Moderate
A right-angled triangle has legs of length 2 cm and 9 cm. Find the length of the hypotenuse, rounded to 2 decimal places. Q8Moderate
A right-angled triangle has legs of length 6 cm and 11 cm. Find the length of the hypotenuse, rounded to 2 decimal places. Q9Challenging
A square has area 49 cm². Find the length of its diagonal, rounded to 2 decimal places. Q10Challenging
A rectangle has area 60 cm² and length 10 cm. Find the length of its diagonal, rounded to 2 decimal places. Q11Challenging
The area of a right-angled triangle is 30 cm². The shorter leg is 5 cm. Find the length of the hypotenuse. Q12Challenging
A right-angled triangle has legs in the ratio 3:4. The shorter leg is 9 cm. Find the length of the hypotenuse. Finding unknown sides
Q13Straightforward
A right-angled triangle has a hypotenuse of 5 cm and one leg of 3 cm. Find the length of the other leg. Q14Straightforward
A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the length of the other leg. Q15Straightforward
A right-angled triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg. Q16Straightforward
A right-angled triangle has a hypotenuse of 17 cm and one leg of 8 cm. Find the length of the other leg. Q17Moderate
A right-angled triangle has a hypotenuse of 10 cm and one leg of 4 cm. Find the length of the other leg, rounded to 2 decimal places. Q18Moderate
A right-angled triangle has a hypotenuse of 8 cm and one leg of 3 cm. Find the length of the other leg, rounded to 2 decimal places. Q19Moderate
A right-angled triangle has a hypotenuse of 12 cm and one leg of 5 cm. Find the length of the other leg, rounded to 2 decimal places. Q20Moderate
A right-angled triangle has a hypotenuse of 15 cm and one leg of 7 cm. Find the length of the other leg, rounded to 2 decimal places. Q21Challenging
A rectangle has a diagonal of 13 cm and a length of 12 cm. Find the width of the rectangle. Q22Challenging
A ladder 15 m long leans against a vertical wall. The foot of the ladder is 6 m from the base of the wall. How high up the wall does the ladder reach? Round your answer to 2 decimal places. Q23Challenging
A right-angled triangle has a hypotenuse of 20 cm and its two shorter sides are in the ratio 3:4. Find the length of the shorter side. Q24Challenging
A right-angled isosceles triangle has a hypotenuse of 10 cm. Find the length of each equal side, rounded to 2 decimal places. Applications of Pythagoras' theorem
Q25Straightforward
A rectangle has length 3 cm and width 4 cm. Find the length of the diagonal. Q26Straightforward
A rectangle has length 5 cm and width 12 cm. Find the length of the diagonal. Q27Straightforward
A rectangle has length 8 cm and width 15 cm. Find the length of the diagonal. Q28Straightforward
A rectangle has length 9 cm and width 40 cm. Find the length of the diagonal. Q29Moderate
Find the distance between the points (0,0) and (6,8). Q30Moderate
Find the distance between the points (1,2) and (4,6). Q31Moderate
Find the distance between the points (0,0) and (5,12). Q32Moderate
Find the distance between the points (2,3) and (10,9). Q33Challenging
A ladder 10 m long leans against a vertical wall. The foot of the ladder is 6 m from the base of the wall. How high up the wall does the ladder reach? Give your answer in metres. Q34Challenging
A rectangular television screen is 80 cm wide and 45 cm tall. Find the length of the diagonal, correct to 2 decimal places. Q35Challenging
A ship travels 9 km north and then 12 km east. How far is the ship from its starting point? Give your answer in kilometres. Q36Challenging
A ramp rises 0.8 m vertically over a horizontal distance of 1.5 m. Find the length of the ramp surface in metres. Worked solutions and answers at openmath.au/year-7/pythagoras-theorem