Question

Given that Y and X are midpoints of triangle UVW , find YX.

Answer 1

YX = 3

Explanation:

In the figure attached y and x are the midpoints of UW and UV.

We have to find the measure of YX.

Since in this figure two triangles ΔUXY and ΔUVW are similar triangles.

So their corresponding sides will be in the same ratio.

`(YX)/(WY)=(UY)/(UW)`

`((2x-3))/((x+3))=(4)/(8)`

8( 2x-3 ) = 4 (x+3) [ by cross multiplication]

16x - 24 = 4x + 12

16x - 4x = 24 + 12

12x = 36

x = 3

Now YX = (2x - 3 )

= 2 × 3 - 3

= 6 - 3 = 3

YX = 3