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musiclover10045

Intersecting chord rule:

DK x KB = AK x CK

12 x 4x+1 = 14 x 3+3x

Simplify:

48x +12 = 42x +42

Subtract 12 from each side:

48x = 42x + 30

Subtract 42x from each side:

6x = 30

Divide both sides by 6:

x = 5

Now find the length of KB: 4x +1 = 4(5) +1 = 20 +1 = 21

Now add KB and AK:

21 + 14 = 35

The answer is D. 35

The required length of KB(21) + AK(14) is 35. Option D is correct.

The figure is given,
where AK = 14. DK = 12, KB = 4x+1 and  KC =3+3x.
KB + AK to be determined.

What is the ratio?

The ratio can be defined as the relativeness of the fraction of one quantity towards others.

Here,
The ratio of AK: DK = KB:KC

[tex]14/12= 4x+1/3+3x\\14*(3+3x) = 12*(4x+1)\\2+42x = 48x+12\\42-12=48x-42x\\6x= 30\\x = 5[/tex]

Now,
= KA + KB
= 14 + 4x+1
= 14+ 4(5)+1
= 35

Thus, the required length of KB + AK is 35.

Learn more about ratios here:

brainly.com/question/13419413

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