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Chapter 5: Q. 17 (page 200)

M and N are the midpoints of the legs of trapezoid EFGH. If basesEF炉andHG炉have lengths2r+sand 4r-3s, express the length ofMN炉in terms of r and s .

Short Answer

Expert verified

The length ofMN炉 in terms of r and s is 3r鈭�s.

Step by step solution

01

- Draw the possible diagram of the given problem.

The possible diagram of the given problem is:

It is being given that M and N are the midpoints of the legs of trapezoid EFGH.

It is also being given that EF炉=2r+sand HG炉=4r鈭�3s.

02

- Write the theorem 5-19.

The theorem 5-19 states that the median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths.

03

- Find the length ofMN¯  in terms of r and s.

Therefore, by using the theorem 5-19 it can be obtained that:

MN炉=12(EF炉+HG炉)=12(2r+s+4r鈭�3s)=12(6r鈭�2s)=22(3r鈭�s)=3r鈭�s

Therefore, the length ofMN炉in terms of r and s is 3r鈭�s.

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