Understanding Engineering Mathematics

5.3.5 Similar triangles

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A.The trianglesABCandPQRare similar. Find the lengths of all sides ofPQRfor
the values ofxgiven by (i) 1 cm (ii) 2 cm (iii) 3.5 cm (iv) 4 m:

C

A

R Q

P

x

B

2.1 cm 2.3 cm

3 cm

B.TrianglesABCandPQRare similar. Given thatAB/PQ=p/q, determine all the

sides of both triangles forp/qvalues (i) 3/2 (ii) 7/3 (iii) 3/8:

A

R 2 cm Q

1.7 cm

1 cm

P

C B

5.3.6 The intercept theorem

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Find the missing lengthsx,y,z,uin the figures below, to two decimal places:

(iii) (iv)

(i) (ii)

A

u

x y

z

B

A B

A

C C

D E

4 7

1

D D E

E

2

2.1

2.4^2

1.5

1.5

1

1

1

D E

A

B

B

C C