   Chapter 4.3, Problem 12E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem In Exercises 11 to 14, consider MNPQ with diagonals M P ¯  and  N Q ¯ . When the answer is not a whole number, leave a square root answer. Exercises 11 – 14If QP = 9 and NP = 6, find NQ and MP.

To determine

To find:

NQ and MP of the given rectangle.

Explanation

The basic property of rectangle:

1) All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).

2) All angles are right angles by definition.

3) The diagonals are congruent.

Calculation:

Given: QP = 9 and NP = 6

Consider the rectangle.

To find NQ and MP:

From the property, opposite sides are congruent in rectangle.

So, MN = QP = 9

MQ = NP = 6

Let us take right MPQ.

By using Pythagorean Theorem

MP2=QP2+QM2=92+62=81+36=117MP=117

Let us take right QNP

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