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The dimensions of a triangle are tripled to form a new triangle. If the area of the new triangle is 54 square feet, how many square feet were in the area of the original triangle?

 May 16, 2022
 #1
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Easy!  The area of the original triangle was 54/3 = 18.

 May 16, 2022
 #2
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Yeah thats what I thought but I tried it and it was wrong :(

TheEarlyMathster  May 16, 2022
 #3
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Similar figures have areas that go by the square of the original sides.

 

So, if the two dimensions are each multiplied by 3, the area of the new figure will be 32 or 9 times the area of the original figure.

 

Since the new triangle is 54 square feet, the original triangle will be 54 / 9 = 6 square feet.

 

To check:  assume that the original triangle had a base of 3 feet and a height of 2 feet, resulting in 6 square feet.

Then, the new triangle will have a base of 3 x 3 = 9 feet and a height of 2 x 3 = 6 feet, resulting in 54 square feet.

 May 16, 2022

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