Triangle def is a right triangle. if fe= 8 and de= 6, find df. right triangle is at e

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Triangle def is a right triangle. if fe= 8 and de= 6, find df. right triangle is at e

Given we don't know which is the hypotenuse, either FE is, or DF is. Note it can't be DE as the hypotenuse is the longest side and you already know FE is longer than DE.

According to pythagoras:

either FE² = DE² + DF²

or DF² = DE² + FE²

8² = 6² + x²

x² = 64 - 36

x = √28 = 5.291...

Not one of the given answers so...

x² = 6² + 8²

x² = 36 + 64

x = √100 = 10

B) 10 for the frist one

Answer

Using the Pythagoras theorem;

[tex]\text{Hypotenuse side}^2=\text{Opposite side}^2 + \text{Adjacent side}^2[/tex]

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:

[tex]\text{DE}^2+\text{EF}^2 = \text{DF}^2[/tex]

Substitute the given values we have;

[tex]6^2+8^2 = \text{DF}^2[/tex]

⇒[tex]36+64 = \text{DF}^2[/tex]

⇒[tex]100 = \text{DF}^2[/tex]

Simplify:

[tex]DF = \sqrt{100} = 10[/tex] units

Therefore, the length of DF is, 10 units

[tex][/tex]

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)

[tex]Triangle def is a right triangle. if fe= 8 and de= 6, find df. right triangle is at e[/tex]

The correct answer is 14.

10 possibly (there is no image)

Explanation:

If you know that right triangles are in certain known ratios, one of which is 3:4:5...then 6:8:x must be 10 since each number is multiplied by 2

3x2 = 6

4x2 = 8

therefore 5x2= 10

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)

Answer

Using the Pythagoras theorem;

[tex]\text{Hypotenuse side}^2=\text{Opposite side}^2 + \text{Adjacent side}^2[/tex]

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:

[tex]\text{DE}^2+\text{EF}^2 = \text{DF}^2[/tex]

Substitute the given values we have;

[tex]6^2+8^2 = \text{DF}^2[/tex]

⇒[tex]36+64 = \text{DF}^2[/tex]

⇒[tex]100 = \text{DF}^2[/tex]

Simplify:

[tex]DF = \sqrt{100} = 10[/tex] units

Therefore, the length of DF is, 10 units