Question

If VX is the bisector of V, find the perimeter of VUW.
A 35
B. 46
C. 58
D. 70​

Answer 1

Perimeter of triangle VUW = 70.

Explanation:

Since VX is angle bisector and VX is perpendicular to UW then triangle UVX is congruent to triangle WVX using ASA property.

then UV=WV...(i) {corresponding sides of congruent triangle are equal.}

and UX=WX ...(ii) {corresponding sides of congruent triangle are equal.}

then 3z-4=z+6

3z-z=6+4

2z=10

z=5

then UW=(3z-4)+(z+6)=3(5)-4+(5)+6=22

WV=5z-1=5(5)-1=24

UV=WV=24

Then perimeter of triangle VUW is

UV+WV+UW=24+24+22=70

Hence final answer is:

Perimeter of triangle VUW = 70.

Answer 2

D. 70​

Explanation:

If VX is the bisector of V, then UX=WX.

This implies that:

`3z-4=z+6`

Group similar terms:

`3z-z=4+6`

`2z=10`

z=5

WU=2(z+6)

WU=2(5+6)

WU=2(11)=22 units

VW=VU=5z-1

Put z=5 to get;

VW=VU=5(5)-1

VW=VU=25-1

VW=VU=24

The perimeter of VWU=24+24+22=70 units