SOLUTION: 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 6cm, what is the length of diagonal AC? A _

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Question 1097459: 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 6cm, what is the length of diagonal AC?
A ___8___D
|.................|
|.................|6
|.................|
B------------C (Not to scale)
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

If the diagonal of each square is 6cm, then the length of a side of each square is
6%2Fsqrt%282%29+=+3%2Asqrt%282%29

Call that side length s; then the length and width of the rectangle are 6s and 8s. The diagonal AC of the rectangle is then 10s by the Pythagorean Theorem.

So the length of diagonal AC is
10%2A3%2Asqrt%282%29+=+30%2Asqrt%282%29

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Edge length of square is x=3sqrt%282%29.


AD is 24%2Asqrt%282%29 and DC is 18%2Asqrt%282%29.
Pythagorean Theorem gives you formula for the diagonal AC.

AC%5E2=%2824sqrt%282%29%29%5E2%2B%2818sqrt%282%29%29%5E2
AC%5E2=1152%2B648
AC%5E2=1800
AC=sqrt%28100%2A2%2A3%2A3%29
AC=30%2Asqrt%282%29