Another way of doing it is

Let us name the larger triangle with sides 12, x as ABC with right angle at B. Let us name the smaller triangle with sides 7 and 3 as ADE with right angle at D. Now if you observe ,triangle ABC and ADE are similar. Hence AB/AD = AC/AE. Using Pythagoras theorem AD = root 40.

Now AB/root 40 = 7/12 => AB = 7*(root 40)/12.

Now again using Pythagoras on the triangle ABC with sides 12, 7*(root 40)/12, x; we get x = 36/7

I added some letters to help guide the solution.



Area of triangle = (1/2)(base)(height)
IMPORTANT CONCEPT: we can use ANY of the three sides as our base.

So, for example, if we want to find the area of triangle ABC, we can use side AB as the base, or we can use side AC as the base, or we can use side BC as the base.

If we use side AB as the base, then the base has length 12 and the height is 3
So, area of triangle ABC = (1/2)(12)(3)

If we use side AC as the base, then the base has length 7 and the height is x
So, area of triangle ABC = (1/2)(7)(x)

IMPORTANT: If we use side AB as the base, the area of the triangle will be the same as the area we get if we use side AC as the base.

So, (1/2)(12)(3) = (1/2)(7)(x) [solve for x]
Divide both sides by 1/2 to get: (12)(3) = (7)(x)
Divide both sides by 7 to get: 36/7 = x

Answer: C

Cheers,
Brent

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