Question

Find the missing segment in the attached image

Answer 1

Answer:

The length of the missing segment is 24

Step-by-step explanation:

Given

The figure above

Required

Determine the missing segment

Let the missing segment be represented with x

Given that, there exist parallel lines between the two triangles;

The relationship between the sides of the triangles is as follows;

$\frac{15}{x} = \frac{15+5}{8+x}$

$\frac{15}{x} = \frac{20}{8+x}$

Cross Multiply

$15 * (8 + x) = 20 * x$

Open bracket

$15*8 + 15 * x = 20 * x$

$120 + 15x = 20x$

Subtract 15x from both sides

$120 + 15x -15x= 20x-15x$

$120 = 20x-15x$

$120 = 5x$

Divide both sides by 5

$\frac{120}{5} = \frac{5x}{5}$

$\frac{120}{5} = x$

$24 = x$

$x = 24$

Hence, the length of the missing segment is 24