Chapter 4.CR, Problem 21CR

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# Review ExercisesIn trapezoid M N O P , M N - ∥ P O - and R and S are the mid-points of M P - and N O - respectively. Find the lengths of the bases if R S   =   15 , M N   =   3 x + 2 , and P O   =   2 x - 7 .

To determine

To Find:

The length of the bases of the trapezoid provided the lengths of its median and length of the bases in expression.

Explanation

Definition:

When the midpoints of the two legs of a trapezoid are joined, the resulting line segment is known as the median of the trapezoid.

Theorem on Trapezoid:

The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases. That is, the length of the median of a trapezoid is the average of the lengths of the bases. Where m is the length of the median and b1 and b2 are the lengths of the bases, m=12(b1+b2); equivalently, m=b1+b22.

Calculation:

It is given that MNOP is a trapezoid with MN-âˆ¥PO- and R and S are the mid-points of MP- and NO- respectively.

By the definition of median, RS is the median of the trapezoid MNOP.

It is provided that RSÂ =Â 15 units. Since the line MN and PO are parallel, they must be the base lengths of the trapezoid MNOP.

Also provided that the base lengths of the trapezoid are MNÂ =Â 3x+2, and POÂ =Â 2x-7

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