Question

This is a question on proportions in geometry. Image has been shared.

Answer 1

(a + b)/(2a - b) = 5/4 b/(a + 9) = 5/9

4*(a + b) = 5*(2a - b)

4a + 4b = 10a - 5b

4a - 10a = -5b - 4b

-6a = -9b

6a = 9b............(a)


b/(a + 9) = 5/9

9*b = 5*(a + 9)

9b = 5a + 45 Recall from (a) 9b = 6a

6a = 5a + 45

6a - 5a = 45

a = 45

9b = 6a

9b = 6*45

b = 6*45/9 = 30

a = 45, b = 30

Answer 2

a+b 5
------- = ---
2a-b 4

b 5
-------- = ---- => 9b = 5a+45 => b = (5a+45)/9
a+9 9


a+b 5
------- = --- => 4a+4b = 10a-5b
2a-b 4

9b = 6a

9(5a+45) =6a divide both sides by 3

3(5a+45) = 2a

15a +135 = 2a

13a = -135

a = -135/13 = -10,38

a= -10,38

9b=6a

3b=2a

3b = 2(-10,38)

3b = -20,76

b = -20,76/3

b = -6,92

hope this helped