Final answer:
The length of su in the isosceles trapezoid STUV is equal to the length of the diagonal SV. The length of su, represented by x√5/2
Step-by-step explanation:
In an isosceles trapezoid where the bases are parallel, the diagonals are of equal length. Let's denote the length of the diagonal SV as x. In an isosceles trapezoid, the diagonals bisect each other at right angles. Therefore, we can determine that SW = WV = x/2.
Now, considering triangle SUW, we have the known length of SW as x/2 and the length of UW as the other diagonal, which is also x. Using the Pythagorean theorem, we can find the length of SU.
Applying the theorem:
SU² = SW² + UW²
SU² = (x/2)² + x²
SU² = x²/4 + x²
SU² = 5x²/4
Taking the square root of both sides:
SU = √(5x²/4)
SU = x√5/2
Therefore, the length of su, represented by x√5/2, equals half the length of the diagonal SV. This concludes that the length of su in the isosceles trapezoid STUV is equal to the length of the diagonal SV.