Math Trigonometry question

[Habeba]

If anyone can help with this, it would be appreciated.

If the projections of the legs onto the hypotenuse in a right triangle are, respectively, 6 cm and 12 cm, then the triangle’s area is equal to:
A: 18 cm2
B: 18√2 cm2
C: 54√2 cm2
D: 36√3 cm2
E: 18√3 cm2

[Juliette]

Hi!

i used (projection1/altitude)=(altitude/projection2)
so 6/a=a/12
square root of 72=a
6 * square root of 2=a

A = (6 * 6 * square root of 2)/2 + (12 * 6 * square root of 2)/2
A = 54 * square root of 2

Hope this helps!!

[Habeba]

Thank you very much!!