Question

If triangle VWZ is congruent to triangle XWY, find the length of YX.

Answer 1

Answer:

Measure of side YX is 22 units.

Step-by-step explanation:

Since ΔVWZ ~ ΔXWY, their corresponding sides will be in the same ratio.

$\frac{VW}{XW}=\frac{VZ}{XY}=\frac{WZ}{WY}$

By substituting the values given in the picture in the ratio,

$\frac{45}{30}=\frac{(3x-9)}{(x+8)}=\frac{36}{24}$

$\frac{(3x-9)}{(x+8)}=\frac{3}{2}$

By cross multiplication,

2(3x - 9) = 3(x + 8)

6x - 18 = 3x + 24

(6x -18) + 18 = 3x + 24 + 18

6x - 3x = (3x + 42) - 3x

6x - 3x = 42

3x = 42

x = $\frac{42}{3}$

x = 14

m(YX) = x + 8

          = 14 + 8

          = 22

Therefore, measure of side YX is 22 units.

Answer 2

The length of XY is 22 units

What is Congruence?

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Give: ΔVWZ ~ ΔXWY, then the corresponding sides will be in the equal ratio.

VW/XW= WZ/WY= ZV/YX

we have,

VW=45, XW= 30, VZ= 3x-9, YX= x+8

So,

VW/XW= ZV/YX

45/30= 3x-9/ x+8.

3/2= 3x-9/ x+8.

2(3x - 9) = 3(x + 8)

6x - 18 = 3x + 24

(6x -18) + 18 = 3x + 24 + 18

6x - 3x = 42

3x = 42

x = 42/3

x = 14

Hence, length YX = x + 8

       = 14 + 8

        = 22 units.

Learn more about Congruence here:

https://brainly.com/question/7888063

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