Similar Triangle: side and area ratio

[m_maskara]

The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?

(1) Angles ABC and KLM are each equal to 55 degrees.

(2) LM is 6 inches.

I do understand that option "A" is correction choice. However, I am trying to understand if a shorter method could be used to determine the correct option.

if sides are in ratio a:b, then the area would be in ratio a^2 : b^ 2.
Since ratio of the area is given as 4. Could I use these two information to determine that the ratio of AB : KL = 2 and so #1 is sufficient.

[Ben Ku]

A short cut to this idea is to know that the ratio of areas of two similar figures is the square of the ratio of lengths of two figures.

For example, in two circles, if the ratio of their ratios are 1:3, then the ratio of their areas is 1:9.

In the problem, if the ratio of the areas of KLM to ABC is 1:4, then the ratio of their hypotenuses is 1:2

Statement (1) is sufficient because it tells us that the two right triangles are similar.

[niharika.jain03]

If the area is 4 times greater than the area of the triangle , then the ratio should be 1:5?

[jnelson0612]

If the area is 4 times greater than the area of the triangle , then the ratio should be 1:5?

The ratio of the smaller triangle's area to the larger triangle's area would indeed be 1:5, given the wording.