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Chapter 5: Q9 (page 192)

Each diagram shows a trapezoid and its median. Find the value of x.

Short Answer

Expert verified

The value of x is 6.

Step by step solution

01

Step 1. Label the diagram.

02

Step 2. Apply the property of trapezoid.

The length of the median of the trapezoid is equal to the average length of the two bases.

From the given figure it can be observed that XY is the median and ABandCDare the two bases of the trapezoid. Therefore, the length of the median is given by

XY=12AB+CD

03

Step 3. Description of step.

Substitute 5x+12 for AB, 3x for CD, and 5x for XY into equation obtained in step 2 to find the value of x.

5x=125x+12+3x10x=8x+122x=12x=6

Therefore, the value of x is 6.

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