Question

In the diagram of equilateral triangle ABC shown

below, E and F are the midpoints of AC and BC,
respectively.
If EF = 2x + 8 and AB = 7x - 2, what is the
perimeter of trapezoid ABFE?
1) 36
2) 60
3) 100
4) 120​

Answer 1

the answer is 100....... ...

Answer 2

Perimeter of trapezoid ABEF= 16x +4

Explanation:

Since it is an equilateral triangle

AC = BC = BC = 7x - 2

Point E and F is formed at mid point of line AC and BC respectively.

Therefore AE = 1/2 x AC and BF = 1/2 x BC

Perimeter of trapezoid ABEF = AB + EF + AE + BF

AB = 7x - 2

EF = 2x + 8

AE = (7x - 2)/2

BF = (7x - 2)/2

Perimeter = 7x - 2 + 2x + 8 + (7x - 2)/2 + (7x - 2)/2

= 7x - 2 + 2x + 8 + 7x - 2

= 7x + 2x + 7x - 2 + 8 - 2

Perimeter of trapezoid ABEF= 16x + 4