Chapter 59 Pythagoras Exerise 1 1. Find : Calulators should not be used anywhere in this Chapter unless you are otherwise instruted. (a) 3 2 (b) 5 2 () 2 2 (d) 1 2 (e) 10 2 (f) 9 2 (g) 11 2 (h) 12 2 (i) 20 2 (j) 100 2 (k) ( 1 2 )2 (l) ( 1 3 )2 (m) ( 1 5 )2 (n) (0 1) 2 (o) (0 01) 2. 2. Calulate the area of a square with side : (a) 5 m (b) 10 m () 7 mm (d) 0 5 m (e) 1 km. Exerise 2 1. Find : (a) 36 (b) 25 () 100 (d) 169 (e) 4 (f) 225 (g) 10000 (h) 900 (i) 1600 (j) 1. 2. Use a alulator and write down to two deimal plaes : (a) 20 (b) 50 () 56 (d) 179 (e) 14 4. 3. Calulate the length of the side of a square with area : (a) 49 m 2 (b) 81 m 2 () 9 m 2 (d) 1 mm 2 (e) 0 25 m 2. Exerise 3 & 4 1. Use Pythagoras Rule to alulate the length of the hypotenuse in this triangle :- => 2 = a 2 + b 2 => 2 = 3 2 +... => 2 = 9 +... =... => =... =... m 4 m 3 m this is Chapter Fifty Nine page 83 PYTHAGORAS
2. For eah right angled triangle shown, use Pythagoras Theorem to alulate the length of eah hypotenuse : (a) (b) () 32 m 12 m 5 m 24 m 9 m 12 m 3. For eah right angled triangle shown, use Pythagoras Theorem to alulate the length of eah hypotenuse (orret to two deimal plaes) : (a) 16 m (b) 20 m () 6 m 14 m 23 m 7 m (d) (e) (f) 16 m 20 m 10 m 9 m 10 m Exerise 5 (In this exerise, round all answers to two deimal plaes where neessary). 1. A metal wire is attahed to the top of a flagpole to help keep it rigid. Calulate the length of the metal wire. (Hint : Use Pythagoras Theorem). 6 5 m 2 8 m this is Chapter Fifty Nine page 84 PYTHAGORAS
2. A long wooden beam is required to prop up a wall whih is deemed unsafe. How long is the required beam? 3 m 6 m 3. A tightrope walker is to walk from 2 8 m a roof-top to the ground along a rope. Calulate the length of the rope. 18 6 m 4. A oloured strip is to be stithed around the outside of the sail of a yaht. 3 5 m Find the total length of strip needed. 4 m 4 m 5. A skateboard ramp has dimensions as shown. 2 m 10 m? m Calulate the length of the sloping side of the ramp. 6. Lines are to be painted in the shape of a large retangle with its diagonals inluded. (a) Calulate the length of one diagonal? (b) What is the total length of the lines requiring to be painted? 14 m 20 m 7. A rhombus has its diagonal lengths 20 entimetres and 14 entimetres. 14 m Calulate the perimeter of the rhombus. 20 m 8. A ship sets out from Port and sails 20 kilometres due West then 15 kilometres due North. The ship develops engine trouble and must return diretly to Port. How far will the ship have to sail to go diretly bak to Port? (A sketh will help you! ) this is Chapter Fifty Nine page 85 PYTHAGORAS
Exerise 6 1. COPY and omplete the alulation to find the length side marked x. a 2 = 2 b 2 => x 2 = 50 2 30 2 => x 2 = 2500 900 50 m x m => x 2 = 1600 => x =... m 30 m 2. In eah of the following right angled triangles, alulate the size of eah unknown smaller side : (Give your answer to two deimal plaes where neessary). (a) 5 m (b) () 7 m 24 m x 13 m 55 m y w (d) 10 m (e) 55 m (f) 7 m z k 90 m 60 m 10 m 3. A triangular garden has dimensions as shown. Find the breadth of the garden.? m 13 m 4. Calulate the height of the tree. 32 m this is Chapter Fifty Nine page 86 PYTHAGORAS
TeeJay Publishers Homework for Level F book Ch 59 - Pythagoras 5. A house has dimensions as shown where the roof is in the shape of an isoseles triangle. 4 5 m Find the total height of the house. 3 m Exerise 7 8 m 1. For eah question below, use an appropriate formula to find the values of x, y and z : (a) 40 m (b) y () 8 6 m x 70 m 7 m 8 m z 15 3 m 2. (a) What is wrong with the triangle shown? (b) In fat, the length of the hypotenuse has been given inorretly. What should its length be? 27 m 23 m 20 m 3. A A farmer has a path whih runs diagonally 50 m aross a retangular field. 160 m B How muh longer is it to walk around the outside of the field from A to B than walking aross the pathway? 4. The top of a ladder is plaed three quarters of the way up an eight foot high wall. Find the length of the ladder. 8 ft 12 ft 5. The road sign is in the shape of an equilateral triangle with side 1 metre. h Find the height of the sign (h metres). 1 m this is Chapter Fifty Nine page 87 PYTHAGORAS
Revision Exerise 1. Find : (a) 8 2 (b) 100 2 () 2. Calulate the length of eah missing side : 100 (d) 12. (a) (b) 29 m () 10 m x m y m 40 m 6 5 m m 3 m 3. A triangular ar window frame needs a rubber seal around its perimeter. Find the perimeter of the window. (Give your answer to the nearest millimetre). 35 m 4. A design for a bridge walkway over a river is as shown. walkway 50 m walkway (river) walkway 25 m 18 m 8 m The arhitet has been given instrutions that the total walkway length must not exeed 100 metres. Has the arhitet designed the bridge properly? (Explain your answer in full showing all working). 5. The area of the triangle shown is 75 m 2. Find the length of the sloping side. this is Chapter Fifty Nine page 88 PYTHAGORAS