Points E,D, and H are the midpoints of the sides of triangle TUV. UV = 46, TV = 56 and HD = 46
To find the length of EH, we need to find the length of TU.
Since E is the midpoint of TV and D is the midpoint of UV, we can use the midpoint formula to find the coordinates of E and D.
Let's let T be the origin (0,0), U be (x_1, y_1), and V be (x_2, y_2).
Since E is the midpoint of TV, the coordinates of E are ((x_1+0)/2, (y_1+0)/2) = (x_1/2, y_1/2).
Since D is the midpoint of UV, the coordinates of D are ((x_2+x_1)/2, (y_2+y_1)/2).
Since H is the midpoint of TU, the coordinates of H are ((x_2+0)/2, (y_2+0)/2) = (x_2/2, y_2/2).
Since HD = 46, we can use the distance formula to find the length of HD:
√((x_2/2 - (x_2+x_1)/2)^2 + (y_2/2 - (y_2+y_1)/2)^2) = 46
Simplifying this equation, we get:
√((x_2 - (x_2+x_1))^2 + (y_2 - (y_2+y_1))^2) = 46
√((x_2 - x_2-x_1)^2 + (y_2 - y_2-y_1)^2) = 46
√((-x_1)^2 + (-y_1)^2) = 46
√(x_1^2 + y_1^2) = 46
Since we know that TU = 56, we can use the distance formula again to find the length of EH:
√((x_1/2 - 0)^2 + (y_1/2 - 0)^2) = √((x_1^2/4) + (y_1^2/4))
Therefore, EH = √((x_1^2/4) + (y_1^2/4))
So, by finding the value of x_1 and y_1 that satisfy the equation √(x_1^2 + y_1^2) = 46 and substituting these values into the equation for EH, we can find the length of EH.