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CBSE Class 10 Answered

Let ABC be a triangle with angleB = 90°. Let AD be a bisector of angleA with D on BC. Suppose AC = 6cm and area of ∆ADC being 10 cm^2. Find the length of BD.  
Asked by acv27joy | 13 Dec, 2018, 07:48: PM
answered-by-expert Expert Answer
Let us draw a line DE perpendicular to AC.
Area of ΔADC = (1/2)×AC×DE = 10cm2
 
(1/2)×6×DE = 10  or DE = (10/3) cm
 
It can be seen from figure, ΔABD and ΔAED are congruent.
(Both are right triangles. begin mathsize 12px style angle end styleBAD = begin mathsize 12px style angle end styleDAE because AD is bisector of begin mathsize 12px style angle end styleA. AD is common side)
Hence BD = DE = (10/3) cm ≈ 3.33 cm
Answered by Thiyagarajan K | 13 Dec, 2018, 09:06: PM

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