Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Question
Chapter 16.4, Problem 3PS
To determine
To find: the perimeter of the quadrilateral EFGH which is inscribe in the
Expert Solution & Answer
Answer to Problem 3PS
The perimeter is 60.8 .
Explanation of Solution
Given:
Quadrilateral EFGH having EF=7,GH=20 and EH=25.
Concept used:
Ptolemy’s theorem:
For a cyclic quadrilateral or quadrilateral which inscribe in a circle then the sum of the products of the two pairs opposite side equals the product of the diagonal.
Mathematically,
AC.BD=AB.CD+AD.BC .
Calculation:
According to the given:
Quadrilateral EFGH having EF=7,GH=20 and EH=25.
Using Ptolemy theorem:
15×24=7×20+25×x.x=8.8.
So, the perimeter of the quadrilateral is sum of all side of the quadrilateral which means:
EF+FG+GH+EH=7+8.8+20+25=60.8 .
Hence, the perimeter is 60.8 .
Chapter 16 Solutions
Geometry For Enjoyment And Challenge
Ch. 16.1 - Prob. 1PSCh. 16.1 - Prob. 2PSCh. 16.1 - Prob. 3PSCh. 16.1 - Prob. 4PSCh. 16.1 - Prob. 5PSCh. 16.1 - Prob. 6PSCh. 16.1 - Prob. 7PSCh. 16.1 - Prob. 8PSCh. 16.1 - Prob. 9PSCh. 16.1 - Prob. 10PS
Ch. 16.1 - Prob. 11PSCh. 16.1 - Prob. 12PSCh. 16.2 - Prob. 1PSCh. 16.2 - Prob. 2PSCh. 16.2 - Prob. 3PSCh. 16.2 - Prob. 4PSCh. 16.2 - Prob. 5PSCh. 16.3 - Prob. 1PSCh. 16.3 - Prob. 2PSCh. 16.3 - Prob. 3PSCh. 16.3 - Prob. 4PSCh. 16.3 - Prob. 5PSCh. 16.4 - Prob. 1PSCh. 16.4 - Prob. 2PSCh. 16.4 - Prob. 3PSCh. 16.4 - Prob. 4PSCh. 16.4 - Prob. 5PSCh. 16.5 - Prob. 1PSCh. 16.5 - Prob. 2PSCh. 16.5 - Prob. 3PSCh. 16.5 - Prob. 4PSCh. 16.5 - Prob. 5PSCh. 16.6 - Prob. 1PSCh. 16.6 - Prob. 2PSCh. 16.6 - Prob. 3PSCh. 16.6 - Prob. 4PSCh. 16.6 - Prob. 5PSCh. 16 - Prob. 1RPCh. 16 - Prob. 2RPCh. 16 - Prob. 3RPCh. 16 - Prob. 4RPCh. 16 - Prob. 5RPCh. 16 - Prob. 6RPCh. 16 - Prob. 7RPCh. 16 - Prob. 8RPCh. 16 - Prob. 9RPCh. 16 - Prob. 10RPCh. 16 - Prob. 11RPCh. 16 - Prob. 12RPCh. 16 - Prob. 13RP
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