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Chapter 5: Q2 (page 192)

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

Short Answer

Expert verified

The value of x is 19.

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 FC is the median and AB and EDare the two bases of the trapezoid. Therefore, the length of the median is given by

FC=12AB+ED

03

Step 3. Description of step.

Substitute 25 for AB, 13 for ED and x for FC into the equation obtained in step 2 to find the value of x.

x=1225+13=12×38=19

Therefore, the value of x is 19.

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Most popular questions from this chapter

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

∠SKC≅∠CAS;∠KCA≅∠ASK

M, N and T are the midpoints of the sides of ΔXYZ.

If TN=7, thenXY=?¯

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 5-5.

M, N and T are the midpoints of the sides of ΔXYZ.

If XY=k, thenTN=?¯

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

AD¯∥BC¯
See all solutions

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