Question

Triangle DEF is a right triangle. if FE= 8 and DE= 6, find DF. right triangle is at E

Answer 1

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

Answer 2

Use the Pythagorean  theorem
a^2 +b^2 = c^2.
 In this case, 'a' would be FE and 'b' would be 6
. Therefore,
8^2 + 6^2 =c^264 + 36 =c^2 100 = c^2   10 = c  (which would correspond to DF)