Question

Points D and E are midpoints of the sides of triangle ABC. The perimeter of the triangle is 48 units. What is the value of t?

A) 2
B) 3
C) 4t
D) 3t

Answer 1

In a triangle, if D and E are the midpoints of the sides, then DE is parallel to the third side. This means that DE is half the length of the third side. Using this information, we can solve for t in the equation A + DE + DE = 48, which represents the perimeter of the triangle.

Step-by-step explanation:

In a triangle, if D and E are the midpoints of the sides, then DE is parallel to the third side. This means that DE is half the length of the third side.

Let t be the length of the third side. Since the perimeter of the triangle is 48 units, the sum of the lengths of the sides is 48. So, A + B + C = 48.

Since DE is half the length of the third side, DE = t/2.

Because DE is parallel to the third side, we can say that DE is equal to either A or B. So, DE = A = t/2.

Using the information given, we have A + DE + DE = 48. Substituting t/2 for both A and DE, we get t/2 + t/2 + t/2 = 48. Simplifying this equation, we find 3t/2 = 48. Solving for t, we get t = (48 x 2)/3 = 32.

Therefore, the value of t is 32, which means the correct answer is option D) 3t.