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A six by eight grid is constructed with 48 small squares in a rectangle, as illustrated. If the diagonal of one of the small squares is 6 cm, what is the length of the diagonal \(\bar{AC}\)?

 

A   _________8_________  D

   |

   |

6 |

   |

   |

 B  |___________________| C

 

Thanks!

 Sep 8, 2019
edited by Guest  Sep 8, 2019
 #1
avatar+103858 
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We can construct the following rectangle  ABCD  with squares of side 1

 

 

The length of the diagonal  of  one of these squares =  √[1^2 + 1^2] = √2

 

And the diagonal AC of the image  = √[6^2 + 8^2]  = √100  =  10

 

Since these are similar figures, we can solve for the diagonal length of your problem, AC, thusly

 

6 / √2 =    AC / 10         cross-multiply

 

10*6 / √2  =  AC    =    60/√2  =  60√2/ 2   =  30√2

 

 

cool cool cool

 Sep 8, 2019
 #2
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Thank you!

 Sep 9, 2019

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