Question

If 3.6h = 1.6k, then find (h-k)/(h+k)

Answer 1

SOLUTION

GIVEN

3.6h = 1.6k

TO EVALUATE

$\displaystyle \sf{ \frac{h - k}{h + k} }$

EVALUATION

Here it is given that

$\displaystyle \sf{ 3.6h = 1.6k}$

$\displaystyle \sf{ \implies \frac{h}{k} = \frac{1.6}{3.6} }$

$\displaystyle \sf{ \implies \frac{h}{k} = \frac{16}{36} }$

$\displaystyle \sf{ \implies \frac{h}{k} = \frac{4}{9} }$

Now Componendo and Dividendo rule we get

$\displaystyle \sf{ \implies \frac{h + k}{h - k} = \frac{4 + 9}{4 - 9} }$

$\displaystyle \sf{ \implies \frac{h + k}{h - k} = \frac{13}{ - 5} }$

$\displaystyle \sf{ \implies \frac{h - k}{h + k} = \frac{ - 5}{ 13} }$

$\displaystyle \sf{ \implies \frac{h - k}{h + k} = - \frac{ 5}{ 13} }$

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Answer 2

Given:

3.6h =  1.6k

To find :

$\frac{h - k}{h + k}$

Solution:

Step 1 of 2:

From the given values we get ,

3.6 h = 1.6 k

h  =  $\frac{1.6}{3.6}$ k

h = $\frac{1.6}{3.6}$× $\frac{10}{10}$ k

h = $\frac{16}{36}$ k

h = $\frac{4}{9}$ k

Step 2 of 2:

On substituting the value of h,

$\frac{h - k}{h + k}$ = $\frac{\frac{4}{9} k - k}{\frac{4}{9} k + k}$

$\frac{h - k}{h + k}$  = $\frac{\frac{4k - 9 k}{9} }{\frac{4k + 9k}{9} }$

$\frac{h - k}{h + k}$ = ${\frac{4k - 9 k}{9}$ ×  ${\frac{9}{4k + 9 k}$

$\frac{h - k}{h + k} = \frac{-5k}{13k}$

$\frac{h - k}{h + k} = \frac{-5}{13}$

Final answer:

The value of $\frac{h - k}{h + k}$  is $- \frac {5}{13}$ .