Mathematics: Find the missing value 8 14 45 15

Find the missing value 8 14 45 15 - id81445152562388, hanglenn1

Ответ:

ebh3

03.01.2022

The correct option is B.

Step-by-step explanation:

From the given figure it is nices that the length of sides AB, BC and AC are 20, 22 and 35. The line AD is angle bisector.

Let the missing value be x.

The Triangle Angle Bisector Theorem states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Since AD is angle bisector, therefore

$\frac{AB}{AC}=\frac{BD}{CD}$

$\frac{20}{35}=\frac{22-x}{x}$

20x=35(22-x)

20x=770-35x

Add 35x both sides.

55x=770

Divide both sides by 55.

$x=\frac{770}{55}$

x=14

Therefore, second option is correct.

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Find the missing value
8
14
45
15

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