Chapter 8.2, Problem 40E

### 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

# Square RSTV is inscribed in square WXYZ, as shown. If Z T = 8 and T Y = 15 , Finda) the perimeter of RSTVb) the area of RSTV

To determine

To Find:

a. The perimeter of the square RSTV.

b. The area of the square RSTV.

Explanation

Formula Used:

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

AC2=AB2+BC2.

2. The perimeter of a polygon is the sum of the lengths of all sides of the polygon. P=4s, where s is side length of the square.

3. Area of the square =s2, where s is side length of the square.

It is given that the square RSTV is inscribed in square WXYZ with ZT=8 and TY=15.

The side ZY is split into ZT and TY with dimension 8 and 15 respectively.

As WXYZ is a square, each side of RSTV can also be split into two parts. That is, 8 and 15 respectively. Therefore, ZT=YS=XR=WV=8 and TY=SX=RW=VZ=15

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