Explanation: part (a): getting the value of AE: The two triangles AEB and DEF are similar. Therefore, we can make use of the similar proportionality as follows: AE / DE = BE / FE Now, we have: AE is the unknown we want to find DE = AE + 2 BE = 7.8 ft FE = 7.8 + 2.4 = 10.2 ft
Substitute in the above relation and get the value of AE as follows: AE / DE = BE / FE AE / (AE+2) = 7.8 / 10.2 10.2 AE = 7.8 AE + 15.6 2.4 AE = 15.6 AE = 6.5 ft
Part (b): getting the perimeter of AEB: perimeter = AE + EB + AB perimeter = 6.5 + 7.8 + 4.2 perimeter = 18.5 ft