FIND THE MISSING SIDES USING PYTHAGOREAN THEOREM WORKSHEET

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

The size of a computer monitor is the length across its diagonal. If a computer monitor is 34.4 cm long and 27.5 cm high, what size is it?        Solution

Problem 6 :

(a)  Find the length of the wire shown supporting the TV mast. 

(b) There are six wires which support the mast.

i)  Find their total length.

ii)  If 3% extra wire is needed for tying, how many meters of wire need to be purchased?

Solution

Problem 7 :

Metal supports are made as shown. They are fitted from the lower edge of the table top to the legs. The flat ends of the supports are 2 cm long. Find the length of the metal needed to make the 8 supports used to stabilise the table.

Solution

Problem 8 :

A ladder is 2 meters long. It leans against a wall so the base is 86 cm from the wall. 

a) Write 86 cm in meters. 

b) How far up the wall does the ladder reach?

Solution

Problem 9 :

Heidi has made a rectangular cushion cover which measures 36 cm long by 32 cm wide. She wants to put lace across one diagonal on each side. 

a) Find the length of the diagonal. 

b) Find the total length of lace required, if 4 cm extra is allowed for finishing off the ends.

c) Calculate the cost of the lace at $2.30 per meter

Solution

Problem 10 :

A square garden with sides 100 m is divided into two triangular plots by a fence along one diagonal.

a) What is the length of the fence in meters (to 1 decimal place) ?

b) If the fence costs $15.50 per meter, what is the total cost ?    Solution

Problem 11 :

A 160 m long water pipe runs along the diagonal of a square paddock. What are the lengths of the sides of the paddock?        Solution

Problem 12 :

A garden gate is 1.2 meters wide and 1.2 meters high. The gate is strengthened by a diagonal strut.

a) How long is the strut?

b) Calculate the length of steel needed for the frame of the gate, including the strut.

Solution

Problem 13 :

Solution

Problem 14 :

Solution

Problem 15 :

Solution

Problem 16 :

Solution

Problem 17 :

Solution

Problem 18 :

Answers :

(1)  AC  =  5cm

(2)  AC  =  8.6 cm

(3)  PQ  =  8.1 cm

(4)  SR  =  13.6 cm

(5)  44 cm

(6)  (a)  10.28 m  (b)  61.7 m  (c)  64 m

(7)  145.12 cm.

(8)  1.80

(9)  (a)  48.2 m  (b)  100.4  (c)  $231

(10)  (a)  141.4 m  (b)  $777.7

(11)  113.14 m

(12)  (a)  1.7 m  (b)  6.5 m

(13)  x  =  4.12 cm and y  =  2.8 cm

(14)  x  =  5.38 and y  =  6.70

(15)  x  =  2.23 and y  =  2.44

(16)  x  =  1.414 

(17)   x  = 14 cm

(18)   AC  =  6.24

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