38% 12:19 Mon 18 Jan
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6. In the diagram,
AB = x cm
BC = (x + 5) cm
CD= (2x - 1) cm
AD = 28 cm
D
B
a Show that 4x + 4 = 28
(2 marks)
b Solve 4x + 4 = 28
(2 marks)
c Work out the length of BD.
(2 marks)

The answer is below

Step-by-step explanation:

The line segment addition postulate states that for a line segment AC, another point B lies on AC if the below equation is satisfied:

AB + BC = BC

a) From the question, since point B and C lies on AD, then:

AD= AB + BC + CD

Substituting:

28 = (x) + (x + 5) + (2x - 1)

collecting like terms:

x + x + 2x + 5 - 1 = 28

Simplifying:

4x + 4 = 28

b) Simplifying the equation:

4x + 4 = 28

subtract 4 from both sides:

4x + 4 - 4 = 28 - 4

4x = 24

Divide through by 4:

4x / 4 = 24 / 4

x = 6

c) Also, BD = BC + CD

Hence:

BD = (x  + 5) + (2x - 1)

x + 2x + 5 - 1 = BD

3x + 4 = BD

substitute value of x:

3(6) + 4 = BD

18 + 4 = BD

BD = 22

the answer is b.)

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