SOLUTION: Benjamin visited an art show and saw a painting he really wanted to purchase but it was very expensive! In the gift shop, he found that he could by post cards of the paintings at a

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Question 1030634: Benjamin visited an art show and saw a painting he really wanted to purchase but it was very expensive! In the gift shop, he found that he could by post cards of the paintings at a much more affordable price. The post card was 4 inches by 6 inches and it said that it was 2/7 the size of the original. What are the dimensions of the original painting?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Size is in reference to area, not distances.

4 by 6 is area 4%2A6=24%2Ainch%5E2.

4%2A6=%282%2F7%29A using original area A.

A=%284%2A6%29%287%2F2%29
A=2%2A6%2A7
A=84

Some linear factor k will change 4 by 6 into the area 84.
4k%2A6k=84
4%2A6%2Ak%5E2=84
k%5E2=84%2F%284%2A6%29
k%5E2=%287%2A2%2A6%29%2F%284%2A6%29
k%5E2=%287%2A2%29%2F4
k%5E2=7%2F2
k=sqrt%287%2F2%29
k=sqrt%287%29sqrt%282%29%2F2
k=%281%2F2%29sqrt%2814%29

Original dimensions were highlight%284%281%2F2%29sqrt%2814%29=2sqrt%2814%29%29
and
highlight%286%281%2F2%29sqrt%2814%29=3sqrt%2814%29%29.