Points E,D, and H are the midpoints of the sides of triangle TUV. UV = 120, TV = 148 and HD = 120 find TU
By the midpoint theorem, we know that the length of the side TUV is twice the length of the side E'D, where D and E' are the midpoints of TV and UV, respectively. Thus, we have E'D = (1/2)(120) = 60.
Since D is the midpoint of TV, we have TD = (1/2)(TV) = (1/2)(148) = 74.
Now, we can use the Pythagorean Theorem to find the length of TU. Since E'D is a midsegment of triangle TUV, it is parallel to TU and its length is half the length of TU. Thus, we have E'D = (1/2)TU.
Using the Pythagorean Theorem, we have:
(E'D)^2 + (TD)^2 = TU^2
(60)^2 + (74)^2 = TU^2
3600 + 5476 = TU^2
9076 = TU^2
Taking the square root of both sides, we find:
TU = √9076
Therefore, TU is approximately equal to 95.33.