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Chapter 1: Q39. (page 16)

For the following figure, Eis the midpoint of role="math" localid="1648981591259" DF炉. Find the value z, where GE=z+2, EH=2z鈭�6and GH=20. Find the GE, EHand state whether Eis the midpoint of GH炉.

Short Answer

Expert verified

The value of z is 8, GE=10and EH=10 alsoEis the midpoint of GH炉

Step by step solution

01

Step 1- Apply the concept of the length of the line.

The total length of the line is the sum of the length of all parts of a line.

02

Step 2- Check the figure.

Consider the figure.

Here the length of GHis the sum of GE andEH

03

Step 3- Find the value of  z.

Since GH=GE+EH

Equate the values as follows:

20=z+2+2z鈭�620=3z鈭�4

04

Step 4- Simplify the equation.

Simplify the equation as follows:

20=3z鈭�43z=20+43z=24

Divide the equation both sides by 3.

3z=243z3=243z=8

Therefore, the value ofz is 8.

05

Step 5- Step description.

Find the values of GEand EHas follows:

GE=z+2GE=8+2GE=10

EH=2z鈭�6EH=28鈭�6EH=16鈭�6EH=10

Since the value of GEand EHare same, therefore Eis the midpoint of GH炉.

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