Line PQ is parallel to BC and splits AB into lengths of AP = x + 8 and PB = x. The other side, AC, is split into lengths of
AQ = x + 13 and QC = x + 1. What is the length of AC? Image Not to Scale.
A) 12
B) 14
C) 16
D) 18
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Given : Line PQ is parallel to BC and splits AB into lengths of AP = x + 8 and PB = x. The other side, AC, is split into lengths of
AQ = x + 13 and QC = x + 1.
To Find : the length of AC
A) 12
B) 14
C) 16
D) 18
Solution:
Using BPT ( Thales theorems)
AP/PB = AQ/AC
=> (x + 8)/x = (x + 13)/(x + 1)
=> (x + 8)(x + 1) = x(x + 13)
=> x² + 9x + 8 = x² + 13x
=> 4x = 8
=> x = 2
AC = AQ + QC
= x + 13 + x + 1
= 2x + 14
= 2(2) + 14
= 4 + 14
= 18
Length of AC is 18
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0
Answer:
18
Step-by-step explanation:
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