Respuesta :

Hrishii

Answer:

24

Step-by-step explanation:

In triangle STU, line VT bisects angle STU.

-> By angle bisector theorem:

[tex] \frac{67}{2b} = \frac{67}{b + 24} \\ \\ \implies \: \frac{1}{2b} = \frac{1}{b + 24} \\ \\ \implies \: 2b = b + 24 \\ \\ \implies \: 2b - b = 24 \\ \\ b = 24[/tex]

varshamittal029

The value of b is 24

What is angle bisector theorem ?

If we consider a triangle TSU, Let the angle bisector of angle T intersect side SU at a point V between S and U. The angle bisector theorem states that the ratio of the length of SV to the length of VU is equal to the ratio of the length of ST to the length of TU.

i.e. [tex]\frac{|SV|}{|VU|}=\frac{|ST|}{|TU|}[/tex]

How to find the value of b ?

Here, given that, SV = 2b, VU = b+24, ST = TU = 67

∴ [tex]\frac{|SV|}{|VU|}=\frac{|ST|}{|TU|}[/tex]

⇒ [tex]\frac{2b}{b+24}=\frac{67}{67}[/tex]

⇒ [tex]\frac{2b}{b+24}=1[/tex]

⇒ 2b = b+24

⇒ b = 24

Hence, b = 24

Learn more about Angle bisector theorem here :

https://brainly.com/question/27261528

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