Answer
Using the Pythagoras theorem;
\(\text{Hypotenuse side}^2=\text{Opposite side}^2 + \text{Adjacent side}^2\)
As per the statement:
In a right triangle DEF , right triangle is at E as shown below.
FE = 8 units , and DE = 6 units
Using Pythagoras theorem in triangle DEF:
\(\text{DE}^2+\text{EF}^2 = \text{DF}^2\)
Substitute the given values we have;
\(6^2+8^2 = \text{DF}^2\)
⇒\(36+64 = \text{DF}^2\)
⇒\(100 = \text{DF}^2\)
Simplify:
\(DF = \sqrt{100} = 10\) units
Therefore, the length of DF is, 10 units
