Points D, E and F are the midpoints of the sides of triangle ABC. If AD=6, CF=4 and the perimeter of triangle ABC = 30, then find BE.
If D is between A&B, E is between B&C and F is between C&A, then the perimeter is 6+6+4+4 + (twice length of BE)= 30
Solve that.
The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral.
To find the length of BE, let's start by calculating the sum of the lengths of the sides of triangle ABC.
Given that AD = 6 and CF = 4, we know that DE = EF = FD = (1/2) * (AD + CF). Therefore, DE = EF = FD = (1/2) * (6 + 4) = 5.
We also know that the perimeter of triangle ABC is 30. So, we have:
AB + BC + CA = 30.
Since D, E, and F are the midpoints of the sides of triangle ABC, we can calculate the lengths of the sides of triangle ABC in terms of DE.
AB = 2 * DE = 2 * 5 = 10.
BC = 2 * EF = 2 * 5 = 10.
CA = 2 * FD = 2 * 5 = 10.
Now, we can substitute these values into the perimeter equation:
10 + 10 + 10 = 30.
Therefore, the sum of the lengths of the sides is consistent with the given perimeter.
To find BE, we subtract the lengths of the other sides from the perimeter and then divide by 2 because BE is one of the midpoints:
BE = (30 - AB - BC) / 2.
Substituting the values, we get:
BE = (30 - 10 - 10) / 2 = 10 / 2 = 5.
So, the length of BE is 5.