Question

V and S are the midpoints of the legs, UW and RT, of trapezoid RTUW.

If TU = 22x, SV = 37x, and RW = 2x + 50, what is the value of x?

Answer 1

By applying the midpoint theorem for trapezoids to the given lengths and setting up the equation (22x + (2x + 50)) / 2 = 37x, we find that x = 1.

Step-by-step explanation:

The problem concerns a trapezoid with midpoints V and S on its legs. We are given that TU = 22x, SV = 37x, and RW = 2x + 50. To find the value of x, we can use the properties of a trapezoid with midpoints on its legs.

According to the midpoint theorem for trapezoids, the segment that connects the midpoints of the legs is parallel to both bases and its length is equal to the average of the lengths of the two bases (TU and RW). So we set up the equation:

(22x + (2x + 50)) / 2 = 37x

Solving for x:

1. Combine like terms: 24x + 50 = 74x
2. Subtract 24x from both sides: 50 = 50x
3. Divide both sides by 50: x = 1