SOLUTION: 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

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): You can put this solution on YOUR website!
a=.5bh
a=.5*3*4=6
a=.5*4*12=24 B)
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
RELATED QUESTIONS
What are the dimensions of a right angle triangle that is similar to the 3 -4 -5... (answered by Theo)
Prove that if an acute angle of one right triangle is congruent to an acute angle of... (answered by richard1234)
a) The perimeters of two similar triangles are 110 and 65. If the altitude of the smaller (answered by CubeyThePenguin,greenestamps)
"Sketch a triangle similar to triangle X with an area that is 1/4 the area of triangle... (answered by cleomenius)
A (1,6) , B (-1,4) , C (2,1) are the vertices of a traingle.Show by using distance... (answered by mananth)
Fundamental Ideas Points, Lines, and Planes Postulates and Theorems Segments,... (answered by richard1234)
The hypotenuse and one of the legs of a right triangle form an angle that has a sine of (answered by Alan3354)
if triangle TKM and triangle DAJ are similar what is the measure of angle M, the drawing (answered by josgarithmetic)
A triangle has side lengths of 3 meters , 5 meters ,and 4 meters . the triangle is... (answered by CharlesG2,edjones)