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in the diagram of ∆DEF, the altitude from right angle DFE has been drawn to DE. if DG = 4 and GE = 8, then which of the following is the length of FG?

1)4√2
2)3√10
3)12
4)6​

in the diagram of DEF the altitude from right angle DFE has been drawn to DE if DG 4 and GE 8 then which of the following is the length of FG 1422310312 46 class=

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calculista

Answer:

Option 1. [tex]4\sqrt{2}\ units[/tex]

Step-by-step explanation:

we know that

[tex]<FDE+<FED=90\°[/tex] ----> by complementary angles

and

[tex]<DFG=<GEF[/tex]

so

In the right triangle DFG

[tex]tan(<DFG)=\frac{DG}{FG} =\frac{4}{FG}[/tex] ---> equation A

In the right triangle EFG

[tex]tan(<GEF)=\frac{FG}{GE} =\frac{FG}{8}[/tex] ---> equation B

equate equation A and equation B

[tex]\frac{4}{FG}=\frac{FG}{8}\\ \\FG^{2}=8*4\\ \\FG^{2}=32\\ \\FG=\sqrt{32}\ units\\ \\FG=4\sqrt{2}\ units[/tex]

ashishdwivedilVT

The length of FG in given right-angle triangle is 4√2.

It is given that:

In a right angle triangle DEF

DG=4

GE=8

What is a right-angle triangle?

Right-angle triangle is a triangle in which one angle is a right angle or two sides are perpendicular.

As we know that,

In a right angle triangle,

Square of length of altitude from the right angle is the product of the segments of the hypotenuse i.e.

[tex]FG^{2} = DG*GE[/tex]

[tex]FG^{2} = 4*8\\FG^2 = 32\\FG =4\sqrt{2}[/tex]

Therefore, The length of FG in given right-angle triangle is 4√2.

To get more about right-angle triangle visit:

https://brainly.com/question/15785456

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