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Chapter 5: Q20 (page 193)

For the following figure, given that TA=TB=BCand TD=DE=EF.

Mike makes up a problem for the figure, setting AD=2x+1, BE=4x+2and CF=6x鈭�3 and asking for the value of x. Katie says, 鈥淎nybody can do that.鈥� Explain

Short Answer

Expert verified

This figure is possible for all values of x.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

Consider that TA=AB=BC,TD=DE=EF,AD=2x+1,BE=4x+2,CF=6x+3.

Use the mid-segment or median of the trapezoid as follows:

AD=BE2AD=4x+22AD=2x+1

03

Step 3. Step description.

Similarly,

BE=AD+CF2BE=2x+1+6x+32BE=8x+42BE=4x+2

Therefore, the figure is possible for all values of x.

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