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Chapter 1: Q40. (page 16)

For the following figure, Eis the midpoint of DF炉. Find the value z, where GE=z, EH=2z鈭�4and GH=z+6 . Find the GE, EHand state whether Eis the midpoint of GH炉.

Short Answer

Expert verified

The value of z is 5, GE=5and EH=6, also E is not the midpoint ofGH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 GH is the sum ofGE and EH

03

Step 3-Find the value of z.

Since GH=GE+EH

Equate the values as follows:

z+6=2z鈭�4+zz+6=3z鈭�4

04

Step 4- Simplify the equation.

Simplify the equation as follows:

z+6=3z鈭�4z鈭�3z=鈭�4鈭�6鈭�2z=鈭�10

Divide the equation both sides by -2.

鈭�2z=鈭�10鈭�2z鈭�2=鈭�10鈭�2z=5

Therefore, the value ofz is 5.

05

Step 5- Step description.

Find the values of GEand EHas follows:

GE=zGE=5

EH=2z鈭�4EH=25鈭�4EH=10鈭�4EH=6

Since the value of GEand EHare not the same, therefore Eis not the midpoint of GH炉.

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