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Chapter 5: Q32 (page 194)

For the following figure, given that ABCDis a trapezoid with median MN炉.

If DC=3x,AB=2x2,EF=7 then find the value of x.

Short Answer

Expert verified

The value is x=3.5.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

Since MNis a median therefore

ME=12DC1MF=12AB2

03

Step 3. Step description.

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

EF=MF鈭�MEEF=12AB鈭�12DCEF=12AB鈭�DC

04

Step 4. Step description.

Substitute all the values in the formula EF=12AB鈭�DCand simplify as follows:

EF=12AB鈭�DC7=122x2鈭�3x14=2x2鈭�3x2x2鈭�3x鈭�14=0x2x鈭�7+22x鈭�7=0x+22x鈭�7=0x=鈭�2,72x=鈭�2,3.5

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

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