SOLUTION: What are the dimensions of a right angle triangle that is similar to the 3 -4 -5 Right-angled triangle, and that has an area four times as large? a.4-5-7 b. 4-12-13 c. 6-8-1

Algebra ->  Pythagorean-theorem -> SOLUTION: What are the dimensions of a right angle triangle that is similar to the 3 -4 -5 Right-angled triangle, and that has an area four times as large? a.4-5-7 b. 4-12-13 c. 6-8-1      Log On


   

Question 226386: What are the dimensions of a right angle triangle that is similar to the 3 -4 -5
Right-angled triangle, and that has an area four times as large?
a.4-5-7 b. 4-12-13 c. 6-8-10 d. 9-12-15 e. 12-16-20
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Area equals bh/2

If you double each dimension, you would probably get an area 4 times as large.

Try 6-8-10

base and height will be 3 and 4 in the original triangle to get an area of 12/2 = 6.

base and height will be 6 and 8 in the new triangle to get an area of 48/2 = 24

24/6 = 4 meaning the new triangle area is 4 times as large as the original triangle area.

Your answer should be C.

Your new triangle should also be proportionate to the original triangle.

6-8-10 is exactly double 3-4-5 in the same proportions.

Answer B would give you the same area, but the proportions would be off.

3-4-5 and 4-12-13 do not have the same porportions for all of the dimensions.
4/3 not equal to 2
12/4 not equal to 2
13/5 not equal to 2

Answer C keeps the proportions the same

6/3 = 2
8/4 = 2
10/5 = 2

Keeping the sides in porportions means the angles will stay the same meaning you have the same triangle only larger. The triangle would be similar.