Question

If a:b:c=2:5:7 ,then find the ratio of a square+b sqaure: b square + c square

Answer 1

Answer:

Given a:b:c=2:5:7

Therefore let us take : a=2x , b=5x , c=7x

a square=4 x^2

b square=25 x^2

c square=49 x^2

a square+b square:b square + c square = 4x^2+25x^2:25x^2+49x^2

=29 x^2 : 74 x^2

cutting out x^2

The required ratio will be 29:74

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Answer 2

$\displaystyle \bf ( {a}^{2} + {b}^{2} ) : ( {b}^{2} + {c}^{2} ) = 29 : 74$

Given :

a : b : c = 2 : 5 : 7

To find :

$\displaystyle \sf ( {a}^{2} + {b}^{2} ) : ( {b}^{2} + {c}^{2} )$

Solution :

Step 1 of 2 :

Assume the value of a , b , c

Here it is given that a : b : c = 2 : 5 : 7

Let , a = 2k , b = 5k , c = 7k

Step 2 of 2 :

Find the ratio

$\displaystyle \sf ( {a}^{2} + {b}^{2} ) : ( {b}^{2} + {c}^{2} )$

$\displaystyle \sf =\bigg[ {(2k)}^{2} + {(5k)}^{2}\bigg] : \bigg[{(5k)}^{2} + {(7k)}^{2}\bigg]$

$\displaystyle \sf = (4 {k}^{2} + 25 {k}^{2} ) : (25 {k}^{2} + 49 {k}^{2} )$

$\displaystyle \sf = 29 {k}^{2} : 74 {k}^{2}$

$\displaystyle \sf = 29 : 74$

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