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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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Most popular questions from this chapter

▱DECKis a parallelogram. Complete.

If DE=x+y,EC=12,CK=2x-yand KD=3x-2ythen and x=?,y=?, and the perimeter of▱DECK

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

DX=BX

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-4.

For the following figure, if RE=EWthen name all angles congruent to ∠ERW.
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