   Chapter 8.2, Problem 55E 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

Each side of square R S T V has length 8. Point W lies on V R - and point Y lies on T S - in such a way to form parallelogram V W S Y , which has an area of 16   u n i t s 2 . Find the length of V W - . To determine

To Find:

The length of VW- in the square provided.

Explanation

Formula Used:

1. Pythagorean theorem for the right angle triangle ABC for the hypotenuse AC,

AC2=AB2+BC2.

2. The area A of a square whose sides are each of length s is given by A=s2.

3. The area A of a parallelogram with a base of length b and with corresponding altitude of length h is given by A=bh.

4. Area of right triangle =12bh, where b is the base and h is the height of the triangle.

Calculation:

It is given that Each side of square RSTV has length 8 with point W lies on VR- and point Y lies on TS- in such a way to form parallelogram VWSY.

Also given that area of the parallelogram VWSY is 16 units2.

Since VWSY is a parallelogram, opposite sides are equal in measure. That is, VW = SY.

RW = RV-VW=TS-SY=TY

Since RW = TY, the triangle SRW and the triangle VTY must be same

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