Question

1. What is the value of x ?

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2. What is the value of x?
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3. What is the value of x?
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4. What is the value of x?
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Answer 1

1. x = 94 cm

2. x = 67.5 ft

3. x = 24 mm

4. x = 7 mm

Explanation:

Image 1. In this question we will follow the angle bisector theorem.

"The angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

So that
`(YK)/(KT)=(VY)/(VT)`

`(YK)/(168)=(34)/(95.2)`

`YK = (34)/(95.2)(168)`

`YK = 60 cms`

Therefore x = 34+YK = 34+60 =94 cms

Image 2. Two triangles ΔABM and ΔMNP are congruent.

So by the property all sides will be in the same ratio.

`(AM)/(MN) =(MP)/(MB)`

`[tex](71.5-22)/(71.5)=(x)/(97.5)`

`x=(49.5)/(71.5)(97.5)` =67.5 ft.

Image 3. In two triangles EGD and EDH

`(GD)/(EG)=(DH)/(EH)`

`(x+4)/(44.8)=(35)/(56)`

`x+4 = (35)/(56)(44.8)`

x+4 =28

x = 24 mm

Image 4. In the given triangles
`(5)/(40+5)=(3)/(2x+10+3)`

`(5)/(45)=(3)/(2x+13)`

5(2x+13) = 3×45

10x+65 = 135

10x =135-65

x = 70/10 =7 cm