Pythagoras' theorem test questions

1

What is the length of BC in this right angled triangle to two decimal places?

Right-angled triangle where the hypotenuse, CB, is unknown, side AC equals 6 m, and side AB equals 10 m

136 m

8 m

11.66 m

2

What is the length of the side marked \({x}\), correct to one decimal place?

Right-angled triangle where the hypotenuse equals 16 mm, the short side equals 7 mm, and the long side, x, is unknown

17.5 mm

14.4 mm

4.8 mm

3

My TV measures 30 inches by 20 inches. What is the diagonal length from corner to corner to the nearest inch?

36 inches

22 inches

500 inches

4

A firefighter has a ladder of length 4 m. She needs to reach a window that is 3 m above ground level. How far away from the base of the house does the ladder need to be placed? Please give your answer to 3 decimal places.

A 4 m long ladder leaning against the wall of a house at a point 3 m from the ground. The length from the base of the wall to the base of the ladder is unknown

5 m

2.646 m

3.606 m

5

There are two buildings 10 m apart. One is 9 m high, the other 4 m. What is the diagonal distance between the tops of the two buildings to two decimal places?

Two buildings 10 m apart. One measures 9 m tall, the other 4 m. The diagonal distance between the tops of the two buildings is unknown

13.45 m

9.85 m

11.18 m

6

A sailor starts at the dock, sails 10 km due east and then 7.5 km due south.

What is the shortest distance to sail back to the docks?

6.6 km

12.5 km

17.5 km

7

I am carpeting a bay window using carpet squares measuring 0.8 m × 0.8 m.

A square with two right-angled triangles either side of it

What is the perimeter of the carpeted space?

5.46 m

1.13 m

5.73 m

8

I have a cylindrical pencil case with a diameter of 11.5 cm and a length of 17.25 cm. What is the maximum length pencil that will fit in?

12.86 cm

20.73 cm

17.25 cm

9

Questions 9 - 10 are for Higher tier only

What is the longest length of pole that will fit in a box that measures 20 cm by 5 cm by 7 cm to two decimal places?

A rectangular cuboid measuring 20 cm by 5cm by 7 cm

21.19 cm

20.62 cm

21.77 cm

10

The Great Pyramid has a square base with sides measuring approximately 755 ft and a height of 480 ft. What is the distance from the top of the pyramid to the corner of the base to two decimal places?

A pyramid with a square base measuring 755 ft and a height of 480 ft. The distance from the top of the pyramid to the corner of the base is unknown

717.92 ft

1,067.73 ft

608.46 ft