Question

if a²+b²=1 and a/3=b/4=1/c then find the value of c if c>0​

Answer 1

Step-by-step explanation:

a²+b²=1

a/3=b/4=1/c

a=3b/4

(3b/4)²+b²=1

9b²/16+b²=1

25b²=16

b²=16/25

b=4/5

b/4=4/20=1/5

1/c=1/5

c=5

Answer 2

Answer:

5

Step-by-step explanation:

${a}^{2} + {b}^{2} = 1$

$\frac{a}{3} = \frac{b}{4} = \frac{1}{c}$

Finding a in terms of c,

$\frac{a}{3} = \frac{1}{c} \\ c = \frac{3}{a} \\ a = \frac{3}{c}$

Finding b in terms of c,

$\frac{b}{4} = \frac{1}{c} \\ b = \frac{4}{c}$

Substituting the values,

$( { \frac{3}{c} })^{2} + {( \frac{4}{c} })^{2} = 1 \\ \frac{9}{ {c}^{2} } + \frac{16}{ {c}^{2} } = 1 \\ \frac{9 + 16}{ {c}^{2} } = 1 \\ \frac{25}{ {c}^{2} } = 1 \\ {c}^{2} = 25 \\ \sqrt{ {c}^{2} } = \sqrt{25} \\ c = 5$