In the given figure, PQ and RS are chords of length 10 cm each intersecting at B. If angle PBS = 90° and the area of triangle PBS is 32 cm squared, the length of BR is_____

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Please find below the solution to the asked query:

Given :  PQ = RS  = 10 cm  ,  If angle PBS = 90° , So PB is perpendicular on BS and the area of triangle PBS is 32 cm² 

We know area of triangle  = $\frac{1}{2}$ $\times$ Base $\times$ Height  , 

For triangle we can consider base  =  PB and Height  =  BS and get :

Area of triangle PBS = $\frac{1}{2}$ $\times$ PB $\times$ BS , 
$\frac{1}{2}$ $\times$ PB $\times$ BS = 32 ,

PB $\times$ BS  = 64 

As given PQ = RS  = 10 cm , So PB and BS can't have more than 10  cm, So

We find factors of 64 , As :

64  =  2 $\times$ 32  =  4 $\times$ 16 =  8 $\times$ 8 

Here we can see that only ' 8 ' and  ' 8 '  combination gives value of PB and BS less than ' 10 '  and  ( 8 $\times$  8 = 64 )

So, We can say , PB =  BS  = 8  cm

Therefore,

BR  =  RS -  BS  =  10 -  8 =  2 cm                                                     ( Ans )


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