Question

If a/3 = b/2 = c/5, then what is the value of ratio (c + a)2 : (a + b)2 : (b + c)2?

Answer 1

Answer:

64 :25:49

Step-by-step explanation:

$\frac{a}{3} = \frac{b}{2} = \frac{c}{5} = k \: (let) \\ a = 3k \\ b = 2k \\ c = 5k \\ (c + a) {}^{2} = 64 {k}^{2} \\( a + b) {}^{2} = 25 k {}^{2} \\ (b + c) {}^{2} = 49 k {}^{2}$

(c+a)^2:(a+b)^2:(b+c)^2=64:25:49

Answer 2

Step-by-step explanation:

a/3=b/2

b=2a/3

b/2=c/5

b=2c/5

a/3=c/5

c=5a/3

now. (c+a)2:(a+b)2:(b+c)2

(5a/3+a)2 : (a+2a/3)2 : ( 2c/5+ c)2

(8a/3)2 : (5a/3)2 : ( 2a/3 + 5a/3)2

64a2/9 : 25a2/9 : 49a2/9

64 : 25 : 49