Chapter 5: Q. 17 (page 200)

M and N are the midpoints of the legs of trapezoid EFGH. If bases $\bar{EF}$ and $\bar{HG}$ have lengths $2 r + s$ and $4 r - 3 s$ , express the length of $\bar{MN}$ in terms of r and s .

Short Answer

Expert verified

The length of $\bar{M N}$ in terms of r and s is $3 r - s$ .

Step by step solution

- 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 $\bar{E F} = 2 r + s$ and $\bar{H G} = 4 r - 3 s$ .

- 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.

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

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

$\begin{matrix} \bar{M N} = \frac{1}{2} (\bar{E F} + \bar{H G}) \\ = \frac{1}{2} (2 r + s + 4 r - 3 s) \\ = \frac{1}{2} (6 r - 2 s) \\ = \frac{2}{2} (3 r - s) \\ = 3 r - s \end{matrix}$

Therefore, the length of $\bar{M N}$ in terms of r and s is $3 r - s$ .

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M and N are the midpoints of the legs of trapezoid EFGH. If bases $\bar{EF}$ and $\bar{HG}$ have lengths $2 r + s$ and $4 r - 3 s$ , express the length of $\bar{MN}$ in terms of r and s .

Short Answer

Step by step solution

- Draw the possible diagram of the given problem.

- Write the theorem 5-19.

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

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

Short Answer

Step by step solution

- Draw the possible diagram of the given problem.

- Write the theorem 5-19.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

M and N are the midpoints of the legs of trapezoid EFGH. If bases $\bar{EF}$ and $\bar{HG}$ have lengths $2 r + s$ and $4 r - 3 s$ , express the length of $\bar{MN}$ in terms of r and s .