   Chapter 4.1, Problem 8E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# For Exercises 5 to 8, MNPQ is a parallelogram with diagonals Q N - and M P - . If M R = 5 ( a + 7 ) and M P = 12 a + 34 , find MR, RP, and MP.

To determine

To find:

The lengths of the MR, RP, and MP in the parallelogram MNPQ.

Explanation

Given:

MNPQ is a parallelogram with diagonals QN- and MP- and MR=5(a+7) and MP=12a+34.

Corollary:

The diagonals of a parallelogram bisect each other.

Calculation:

In the given parallelogram MNPQ, given that the diagonals QN- and MP- and MR=5(a+7) and MP=12a+34.

As per the corollary that the diagonals of a parallelogram bisect each other, the diagonals QN- and MP- bisect each other at R.

So MR=RP=12MP

Substituting MR=5(a+7) and MP=12a+34 in MR=12MP

5(a+7)=12×12a+34

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