Step One Show that ΔADC ≡ ΔACB are similar Maybe ≡ this might mean congruent, I'm not sure. I want similarity.
A is common to both triangles. <ADC = <ACB Both angles are right angles. Conclusion ΔADC is similar to ΔACB Angle Angle theorem which is enough to declare similarity.
Step Two Find AB Set up a proportion. AD/AC = AC/AB corresponding parts of similar triangles bear the same ratio.
Substitute and solve for AB 2/5 = 5/AB Cross multiply 2AB = 25 Divide by 2 AB = 13/2 AB = 6.5
Step Three Now you need the height of the triangle (CD) That's just a^2 + b^2 = c^2
a = 2 c = 5 b = ??? 2^2 + b^2 = 5^2 4 + b^2 = 25 Subtract 4 from both sides. b^2 = 25 - 4 b^2 = 21 b = sqrt(21)
Step 4 Find the area. A = 1/2 b*h h = sqrt(21) b = 6.5