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Diketahui persegi panjang dan merupakan titik di dalam persegi panjang. Jika , , dan , maka adalah ....

Diketahui persegi panjang begin mathsize 14px style text ABCD end text end style dan begin mathsize 14px style text P end text end style merupakan titik di dalam persegi panjang. Jika begin mathsize 14px style text PC=8 cm end text end styleError converting from MathML to accessible text., dan Error converting from MathML to accessible text., maka begin mathsize 14px style text PA end text end style adalah .... 

  1. begin mathsize 14px style horizontal ellipsis end style 

  2. begin mathsize 14px style horizontal ellipsis end style 

Jawaban:

Diketahui panjang begin mathsize 14px style text PC=8 cm end text end styleError converting from MathML to accessible text., dan Error converting from MathML to accessible text..

Agar terbentuk segitiga siku-siku, tarik garis tegak lurus dengan titik P seperti garis biru pada gambar. Selanjutnya substitusikan masing-masing diagonal pada persegi ke dalam rumus Pythagoras.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P B squared end cell equals cell a squared plus d squared end cell row cell 7 squared end cell equals cell a squared plus d squared end cell row cell a squared end cell equals cell 7 squared minus d squared space horizontal ellipsis left parenthesis 1 right parenthesis end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell text PD end text squared end cell equals cell b squared plus c squared end cell row cell 4 squared end cell equals cell b squared plus c squared end cell row cell b squared end cell equals cell 4 squared minus c squared space horizontal ellipsis left parenthesis 2 right parenthesis end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P C squared end cell equals cell c squared plus d squared end cell row cell 8 squared end cell equals cell c squared plus d squared end cell row cell c squared end cell equals cell 8 squared minus d squared space horizontal ellipsis left parenthesis 3 right parenthesis end cell end table end style 

Panjang begin mathsize 14px style text PA end text end style dapat dicari dengan mensubstitusikan persamaan (1), (2), dan (3) ke dalam rumus Pythagoras untuk diagonal begin mathsize 14px style text PA end text end style.

 table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px P size 14px A to the power of size 14px 2 end cell size 14px equals cell size 14px a to the power of size 14px 2 size 14px plus size 14px b to the power of size 14px 2 end cell row blank size 14px equals cell begin mathsize 14px style left parenthesis 7 squared minus d squared right parenthesis end style size 14px plus begin mathsize 14px style left parenthesis 4 squared minus c squared right parenthesis end style end cell row blank size 14px equals cell begin mathsize 14px style left parenthesis 7 squared minus d squared right parenthesis end style size 14px plus begin mathsize 14px style left parenthesis 4 squared minus open parentheses 8 squared minus d squared close parentheses right parenthesis end style end cell row blank size 14px equals cell size 14px 7 to the power of size 14px 2 size 14px plus size 14px 4 to the power of size 14px 2 size 14px minus size 14px 8 to the power of size 14px 2 size 14px minus size 14px d to the power of size 14px 2 size 14px plus size 14px d to the power of size 14px 2 end cell row blank size 14px equals cell size 14px 49 size 14px plus size 14px 16 size 14px minus size 14px 64 end cell row blank size 14px equals size 14px 1 row cell size 14px P size 14px A end cell size 14px equals cell size 14px plus-or-minus square root of size 14px 1 end cell row cell size 14px P size 14px A end cell size 14px equals cell size 14px plus-or-minus size 14px 1 end cell row cell size 14px P size 14px A end cell size 14px equals size 14px 1 end table  

Jadi, panjang begin mathsize 14px style text PA end text end style adalah begin mathsize 14px style text 1 cm end text end style.

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