Final answer:
To calculate the perimeter of triangle BED, the length of AD must be known to find side BD using the law of cosines. Side BE is determined using the sine function, and ED is equal to AB. The perimeter is the sum of BE, ED, and BD.
Step-by-step explanation:
The question involves a geometrical problem where a rectangle named ABCD has a side AB of length 1, and angle ABC is trisected by segments BE and BD. To calculate the perimeter of triangle BED, we need to determine the lengths of the sides BD and DE. Given that AB is 1, we can infer that triangle ABE is isosceles with angles of 30 degrees each at A and B (since the angle at B is trisected). Therefore, the length of BE can be found using the sine function: BE = AB / sin(30) = 1 / 0.5 = 2. To find BD, we can apply the law of cosines in triangle ABD: BD = √(AB^2 + AD^2 - 2*AB*AD*cos(60)) = √(1^2 + AD^2 - 2*1*AD*(1/2)) = √(AD^2 + 0.5), where AD is the length of the rectangle's vertical side.
Without the length of AD, we cannot compute the exact perimeter of triangle BED, but with it, we can find BD, add BE, and include side ED (which equals side AB, since ABCD is a rectangle), to get the triangle's perimeter. The perimeter of triangle BED would then be: Perimeter = BE + ED + BD.