The measure of side length x in the right angled triangle is 4.5 units.
The figures in the image are two similar right triangles.
From the image;
Hypotenuse of the small triangle = 4
Leg 1 of the small triangle = 3
Hypotenuse of the larger triangle = 6
Leg 1 of the larger triangle = 3
Since the two right triangles are similar, to solve for length side x, we use proportion.
(Hypotenuse of the small triangle) / (Leg 1 of the small triangle) = (Hypotenuse of the larger triangle) / (Leg 1 of the larger triangle )
Plug in the values and solve for:
4/3 = 6/x
Cross multiplying, we get:
4x = 3 × 6
4x = 18
x = 18/4
x = 4.5
Therefore, the value of x is 4.5.