Question

A line parallel to a triangle's side splits AB into lengths of x − 6 and x + 1. The other side, AC, is split into lengths of x and x + 21. What is the length of AC?

Answer 1

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Answer 2

Answer: Length of AC is 39 units.

Step-by-step explanation:

Since we have given that

Side of triangle ABC , i.e. AB split into lengths of x-6 and x+1

Side AC split into lengths of x and x+21.

So, by using BPT theorem, we get that

$\frac{AD}{DB}=\frac{AE}{EC}\\\\\frac{x-6}{x+1}=\frac{x}{x+21}\\\\(x-6)(x+21)=(x+1)x\\\\x^2-126+15x=x^2+x\\\\14x=126\\\\x=\frac{126}{14}\\\\x=9$

So, Length of AC is given by

$x+x+21\\\\=2x+21\\\\=2\times 9+21\\\\=18+21\\\\=39$

Hence, Length of AC is 39 units.