Pythagoras

Problems

Pythagoras – Problems.

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?

Pythagoras – Problems.

Calculate the value of x in the diagram shown. Give your answer

correct to 1 decimal place. x11cm

6cm

16cm

19cm

9cm

The diagram shows a rhombus with diagonals 19cm and 9cm long. Calculate the length of the side

of the rhombus.

Pythagoras – Problems.

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

wallladder

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?

Pythagoras – Problems.

y

104

x8

Calculate the values of x and y in the diagram shown.

x

9

14 5Use Pythagoras to find the length of the line marked

with an x.

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?

Pythagoras – Problems.

An equilateral triangle has side of length 8cm.

Find the length of the dotted line in the diagram.

B

A

9

C

35

2.8

5.4

6

Find the perimeter of triangle ABC.

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.

Pythagoras – Problems.

10cm

6cm

16cm

The lengths of the diagonals of a kite are 16cm and 6cm respectively. Calculate the lengths of the sides of the kite

Which of the points A(4,5), B(3,-5) and C(-6,2) is furthest away from the origin?

Pythagoras – Problems.

6cm

12cm

4cm

x

3cm

Use Pythagoras to find x.

x

6cm

12cm

5cm

Calculate the length of the side marked x in the diagram shown.

Give your answer correct to 1 decimal place.

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.

Pythagoras – Problems.

12

2x

x

The diagram shows a right angled triangle. Calculate the lengths of the sides of the triangle.