Question 224258: What are the dimensions of a right angle that is similar to the 3-4-5 rightangled 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
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
A triangle similar to a 3-4-5 triangle would have a ratio that is consistent with a 3-4-5 triangle. In other words, if 1 side of the new triangle is doubled, then the other sides of the new triangle should also be doubled. Furthermore, when the area of the larger of 2 similar triangles is quadrupled, its sides were obviously doubled.
The only choice that fits these criteria is CHOICE C. As seen, each of its sides was doubled (2*3=6, 2*4=8, 2*5=10) to form a 6-8-10 triangle.
Now, just to make sure we have the correct choice, we can calculate each area to see if the new and similar 6-8-10 triangle has an area that is 4 times the original 3-4-5 triangle.
Area of 3-4-5 triangle:  square units
Area of 6-8-10 triangle:  square units
It is quite obvious that the 6-8-10 similar triangle's area of 24 square units is 4 times the area of the 3-4-5 similar triangle's area of 6 (24 = 4 * 6)
Therefore, the correct answer is CHOICE 
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