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.