in triangle ABC ,D and E are the midpoint of line AB andAC resp.angle A=angleB=angleC=angleD=60° DE=5cm find the perimeter of triangleABC.
To find the perimeter of triangle ABC, we need to determine the lengths of all three sides. Given that D and E are the midpoints of lines AB and AC respectively, we know that AD = BD = 5cm and AE = EC = 5cm.
Since angle A = angle B = angle C = angle D = 60°, triangle ABC is an equilateral triangle. In an equilateral triangle, all sides are equal in length. Therefore, AC = AB = BC.
To find the perimeter, we can simply add the lengths of all three sides:
Perimeter = AB + BC + AC
Since AB = BC = 2 × AD, we can substitute the values:
Perimeter = 2 × AD + AC
Since AC = 2 × AE, we can further substitute the values:
Perimeter = 2 × AD + 2 × AE
Substituting the given values AD = BD = 5cm and AE = EC = 5cm:
Perimeter = 2 × 5cm + 2 × 5cm
Perimeter = 10cm + 10cm
Perimeter = 20cm
Therefore, the perimeter of triangle ABC is 20cm.
To find the perimeter of triangle ABC, we need to know the lengths of all three sides (AB, BC, and AC).
Given that D and E are the midpoints of AB and AC, we can use the properties of midpoints and the angles in the triangle to find the lengths of the sides.
Since D is the midpoint of AB, we know that AD = DB, and since E is the midpoint of AC, we know that AE = EC.
From the given, we also know that angle A = angle B = angle C = angle D = 60 degrees.
Let's use these facts to find the length of AB and AC:
Since angle A = angle B = 60 degrees, triangle ABD is an equilateral triangle. In an equilateral triangle, all sides are equal, so AB = AD + DB = 2 * AD.
Similarly, since angle A = angle C = 60 degrees, triangle AEC is also an equilateral triangle. Therefore, AC = AE + EC = 2 * AE.
Now, we can calculate the perimeter of triangle ABC:
Perimeter of triangle ABC = AB + BC + AC
Since AB = 2 * AD and AC = 2 * AE, we can substitute these values into the equation:
Perimeter = 2 * AD + BC + 2 * AE
Substituting DE = 5cm and using the fact that AD = DB and AE = EC, we can simplify further:
Perimeter = 2 * 5cm + BC + 2 * 5cm
Perimeter = 10cm + BC + 10cm
Perimeter = 20cm + BC
Therefore, the perimeter of triangle ABC is 20cm + BC. The length of BC is not given in the information provided, so we cannot calculate the exact perimeter without that information.