Question

50. AABC is a right triangle in which <C=90° and CD
AB.If BC= a, CA=b,AB=c and CD= p then prove that
(1) cp= ab (ii) 1/ p2= 1/ a2 + 1/ b2



plzz answer it fast​

Answer 1

Correct question:-

∼ΔABC is a right triangle in which angle C=90° and CD perpendicular AB.If BC= a, CA=b,AB=c and CD= p then prove that (1) cp= ab (ii) 1/ p²= 1/ a² + 1/ b²

Solution:-

i) We have

ar ΔABC= 1/2 ×AB×CD = 1/2 cp ( see figure )

ar ΔABC= 1/2 ×BC×AC=1/2 ab

Therefore,

1/2cp=1/2ab

➠cp= ab

ii) We have

➠cp=ab

➠1/p= c/ab

squaring both side

➠1/p²=c²/a²b²

Now, AB²=AC²+BC²

➠c²= b²+a²

➠1/p²= (b²+a²)/a²b²

➠1/p² = 1/b²+1/a²

Hence, proved