#3**+5 **

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

CPhill
Mar 7, 2016

#3**+5 **

Best Answer

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

CPhill
Mar 7, 2016