Question

A line parallel to a triangle's side splits AB into lengths of x - 7 and x - 3. The other side, AC, is split into lengths of x and x + 12. What is the length of AC?

A) 21
B) 33
C) 54
D)
21
2

Answer 1

Answer:

33

Step-by-step explanation:

Usatestprep

Answer 2

The length of AC is 33. The correct option is B) 33

The diagram that illustrates the question is shown in the attachment below:

From the question,

We are to determine the length of AC.

To determine the length of AC,

First, we will determine the value of x.

From Triangle proportionality theorem,

We have that

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Then, from the diagram, we can write that

$\frac{x-3}{x-7}=\frac{x+12}{x}$

Now, we will solve for x

$\frac{x-3}{x-7}=\frac{x+12}{x}$

This becomes

$x(x-3) = (x-7)(x+12)$

Clearing the brackets

$x^{2} -3x = x^{2} +12x-7x-84$

Simplifying, we get

$x^{2} -3x = x^{2} +5x-84$

Subtract x² from both sides

$x^{2}-x^{2} -3x = x^{2}-x^{2} +5x-84$

$-3x = 5x-84$

Then, subtract and 5x from both sides

$-3x-5x = 5x-5x-84$

$-8x = -84$

Now, divide both sides by -8

$\frac{-8x}{-8}=\frac{-84}{-8}$

∴ $x = 10.5$

From the diagram, we can observe that the length of AC is

AC = x +12 +x

Put the value of x into the above equation

That is,

AC = 10.5 + 12 + 10.5

∴ AC = 33

Hence, the length of AC is 33. The correct option is B) 33

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