Question

In this rectangular box, EF = 16, FD = 5, and DB = 30. Find AF.

Answer 1

Answer:

FA = 25.87  

Step-by-step explanation:

Given: BD = 30 , DF = 5 , EF = 16

To find: FA

Rectangular box is a Cuboid.

Figure attached.

AB = FE = 16

So,

In  ΔADB

using Pythagoras theorem,

$DB^2=AB^2+AD^2\\30^2=16^2+AD^2\\900=256+AD^2\\AD^2=900-256\\AD^2=644\\AD=\sqrt{644}\\AD=2\sqrt{161}$

Again using Pythagoras theorem in Δ ADF we get

$FA^2=DF^2+AD^2\\FA^2=5^2+(2\sqrt{161})^2\\FA^2=25+644\\FA^2=669\\FA=\sqrt{669}\\FA=25.87$

Therefore, FA = 25.87

Answer 2

AD = sqrt(EF^2 + DB^2) = sqrt(16^2 + 30^2) = sqrt(256 + 900) = sqrt(1156) = 34

AF = sqrt(AD^2 + FD^2) = sqrt(34^2 + 5^2) = sqrt(1156 + 25) = sqrt(1181) = 34.4