By the Pythagorean Theorem, we have
c = √ [8^2 + 6^2] = √100 = 10
And by similar triangles, we have
8 / 6 = [ a + 8 ] / 9 cross-multiply
72 = 6 [a + 8 ]
72 = 6a + 48 subtract 48 from both sides
24 = 6a divide both sides by 6
4 = a
And by similar triangles, again, we have
8 / c = [ a + 8 ] / [ b + c ]
8 / 10 = [ 4 + 8 ] / [ b + 10]
4 / 5 = [ 12 ] / [ b + 10 ] cross-multiply
4 [ b + 10 ] = 12 * 5
4b + 40 = 60 subtract 40 from both sides
4b = 20 divide both sides by 4
b = 5
