Question

Am I right?? * Show examples & details if I am wrong!! *

Answer 1

Yes, you are correct.

From the image, we can see 3 triangles, the large triangle and the two triangles that make the larger triangle.

All 3 of these triangles are similar since they're angle measurements are the same (can be proven by geometry).

We can gather the following information from the given information.

• The largest triangle (the one made up of two triangles) has a hypotenuse of 3+9=12, and a leg length of x. The hypotenuse to leg ratio is 12/x

• The second largest triangle has a hypotenuse length x and leg length 9. The hypotenuse to leg ratio is x/9

We know the hypotenuse to corresponding leg ratio must be equal since these two triangles are similar. Thus, we have the equation:

12/x = x/9

Using the cross product property gives us:

x² = 9 × 12

x² = 108

Taking the square root of both sides gives us:

x = √108

= 6 √3

Thus, your answer is correct. Great job!

Let me know if you need any clarifications, thanks!