Question

Use the picture below to answer the following questions.

Answer 1

Step-by-step explanation:

(i)

according to figure 1

AM = CP -------------eq1

given

AM = 2x+3 -------------------eq2

CP = x+4 -------------------eq3

from eq 1,2,3

2x+3 = x + 4

=> 2x-x = 4 - 3

=> x = 1

so

AM = 2x +3= 2*1+3= 5

(ii)

we know SM = CS -------------eq4

and

CM = SM + CS -------------eq5

given

SM = 3x-5 -------------eq6

CS = 2x+11 -------------eq7

so from eq 4,6,7

3x+5 = 2x+11

=> 3x-2x = 11-5

=> x = 6

so SM = 3x-5 = 3*6-5= 13

and CS = 2x+11 = 2*6+11= 23

therefore from eq 5

CM = SM + CS

=> CM = 13 +23

=> CM = 36

(iii)

we know that

AP = CM -------------eq8

given

AP = x -------------eq9

CM = 2x-4 -----------eq10

so

using eq 8,9,10

x = 2x - 4

=> 2x - x = 4

=> x = 4

therefore

AP = x = 4

(iv)

we know that

AP = CM -------------------eq11

and

given

AP = 5x - 8 ---------------eq12

CM = 2x + 1 ---------------eq13

so using eq 11,12,13

5x-8 = 2x+1

=> 5x - 2x = 1+8

=> 3x = 9

=> x = 3

(v)

we know that

AP = CM -------------------eq14

and

given

AP = 3x + 1 ---------------eq15

CM = 8x - 4 ---------------eq16

so using eq 11,12,13

3x + 1 = 8x - 4

=> 8x - 3x = 1 + 4

=> 5x = 5

=> x = 1