Finding the Area of a Similar Right Triangle

[grace77]

For example: if it was given that two right triangles are similar triangles and that the hypotenuse of one is twice as long than the other how would you find the area of the triangle with the twice as long hypotenuse given the area of the other?
Similar right triangles means they are the same corresponding angle? And area of a triangle is 1/2(bxh)
Would really appreciate it if someone could point me in the right direction. Thanks

 

[symbolipoint]

Similar means the angles are congruent between the two figures, and the corresponding sides are in proportion.Imagine two similar right triangles and the sides of the bigger one are each k times the sides of the smaller one.

a=(1/2)bh, and A=(1/2)(kb)(kh).
How do a and A compare?

 

[grace77]

Similar means the angles are congruent between the two figures, and the corresponding sides are in proportion.Imagine two similar right triangles and the sides of the bigger one are each k times the sides of the smaller one.

a=(1/2)bh, and A=(1/2)(kb)(kh).
How do a and A compare?

The base and height would be double due to the ratio right? Therefore the area would be 1/2(2b x2h)

 

[symbolipoint]

The base and height would be double due to the ratio right? Therefore the area would be 1/2(2b x2h)

For your example, yes. My discussion is general. Your example uses, "twice the lengths" but my generalization uses "k times the lengths".