1. Pythagoras
Problems

2. Pythagoras – Problems. It then turns and sails 15km west.
A ship leaves port and sails 18km north.
It then turns and sails 15km west.
How far is the ship from the port?
The hands of a clock are 8.4cm and 5.8cm long.
How far apart are the tips of the hands at 9pm?

3. Pythagoras – Problems. Calculate the value of x in the
11cm
6cm
16cm
Calculate the value of x in the
diagram shown. Give your answer correct to 1 decimal place.
19cm
9cm
The diagram shows a rhombus with
diagonals 19cm and 9cm long.
Calculate the length of the side
of the rhombus.

4. Pythagoras – Problems. and form a triangle.
On square paper plot the points A(-4,2), B(7,-3) and C(3,6)
and form a triangle.
Use Pythagoras to find the perimeter of the triangle. 6m x
wall
ladder
14m
ground 9m
A wall is 6m high.
A ladder 14m long rests against
the wall with the foot of
the ladder 9m from the bottom
of the wall as shown in the diagram.
What length of the ladder x hangs
over the top of the wall?

5. Use Pythagoras to find the length of the line marked
Pythagoras – Problems. y 10 4 x 8
Calculate the values of x
and y in the diagram shown. x 9 14 5
Use Pythagoras to find the
length of the line marked
with an x.

6. Pythagoras – Problems.
If A(1,2), B(5,1) and C(4,-3) are 3 vertices of a
rectangle ABCD, find the coordinates of D.
Draw the rectangle on square paper.
Use Pythagoras to find the lengths of the sides and
the diagonals of the rectangle.
An aero plane leaves an airport and flies
98 km north east. It then turns and flies
114 km south east.
How far is the aero plane from the airport?

7. An equilateral triangle has Find the length of the dotted
Pythagoras – Problems.
An equilateral triangle has
side of length 8cm.
Find the length of the dotted
line in the diagram. B A 9 C 3 5
2.8
5.4 6
Find the perimeter of
triangle ABC.

8. Pythagoras – Problems. The size of a television screen is
given as the size of the diagonal
length of the screen.
If a television screen has a
length of 32 inches and a breadth
of 27 inches, what size screen
does the television have?
42m
25m
70m
16m
35m
goats
pigs
sheep
cows
The diagram shows an arena
used for animals at the
Royal Agricultural Show
at Ingliston.
Calculate the total length of
fencing needed to construct
this arena.

9. Pythagoras – Problems. The lengths of the diagonals
of a kite are 16cm and 6cm
respectively.
Calculate the lengths of the
sides of the kite
10cm
6cm
16cm
Which of the points A(4,5), B(3,-5)
and C(-6,2) is furthest away from the origin?

10. Pythagoras – Problems. Use Pythagoras to find x.
6cm
12cm
4cm x
3cm
Use Pythagoras to find x.
Calculate the length of the side
marked x in the diagram shown.
Give your answer correct
to 1 decimal place. x
6cm
12cm
5cm

11. Pythagoras – Problems. An aero plane flight BA2184 leaves an airport
and flies 90 miles north and
then 80 miles west.
At the same time a second
aero plane Ryan4456 leaves
the airport and flies at the same speed,
60 miles south and then 110 miles east.
How far apart are the two planes at this time?
A circle has a centre C(5,2). The point A(8,6) lies on the circumference of the circle.
Calculate the radius of the circle.
Which of the points P(9,0), Q(2,6) and R(1,1) lie on the circle.

12. Pythagoras – Problems. 12 2x x
The diagram shows a right angled triangle.
Calculate the lengths of the sides of the triangle.