10. 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 ∆PBS is 32 cm²,then the length of BR is =
Answers
Step-by-step explanation:
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 = 12 × Base × Height ,
For triangle we can consider base = PB and Height = BS and get :
Area of triangle PBS = 12 × PB × BS ,
12 × PB × BS = 32 ,
PB × 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 , 64 = 2 × 32 = 4 × 16 = 8 × 8
Here we can see that only ' 8 ' and ' 8 ' combination gives value of PB and BS less than ' 10 ' and ( 8 × 8 = 64 )
So, We can say , PB = BS = 8 cm
Therefore,
BR = RS - BS = 10 - 8 = 2 cm ( Ans )
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