Chapter 5: Q32 (page 194)

For the following figure, given that $A B C D$ is a trapezoid with median $\bar{M N}$ .
If $D C = 3 x, A B = 2 x^{2}, E F = 7$ then find the value of x.

Short Answer

Expert verified

The value is $x = 3.5$ .

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

Since $M N$ is a median therefore

$\begin{array}{l} M E = \frac{1}{2} D C (1) \\ M F = \frac{1}{2} A B (2) \end{array}$

Step 3. Step description.

From the equation (1) and (2) as follows:

$\begin{array}{l} E F = M F - M E \\ E F = \frac{1}{2} A B - \frac{1}{2} D C \\ E F = \frac{1}{2} (A B - D C) \end{array}$

Step 4. Step description.

Substitute all the values in the formula $E F = \frac{1}{2} (A B - D C)$ and simplify as follows:

$\begin{matrix} E F = \frac{1}{2} (A B - D C) \\ 7 = \frac{1}{2} (2 x^{2} - 3 x) \\ 14 = 2 x^{2} - 3 x \\ 2 x^{2} - 3 x - 14 = 0 \\ x (2 x - 7) + 2 (2 x - 7) = 0 \\ (x + 2) (2 x - 7) = 0 \\ x = - 2, \frac{7}{2} \\ x = - 2, 3.5 \end{matrix}$

Since a side cannot be negative therefore the value of x is $3.5$ .

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For the following figure, given that $A B C D$ is a trapezoid with median $\bar{M N}$ .
If $D C = 3 x, A B = 2 x^{2}, E F = 7$ then find the value of x.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

Step 4. Step description.

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For the following figure, given that ABCDis a trapezoid with median MN¯.If DC=3x,AB=2x2,EF=7 then find the value of x.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

Step 4. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

For the following figure, given that $A B C D$ is a trapezoid with median $\bar{M N}$ .
If $D C = 3 x, A B = 2 x^{2}, E F = 7$ then find the value of x.