Question

Q 1. Rationalise the denominator of 1/√2+√3 and hence find its value, if √2= 1.1414 and √3=1.732

Q 2. LMN is a triangle in which altitudes MP and NQ to sides LN and LM respectively are equal. Show that Δ LMP is congruent to ΔLNQ and LM=LN.

Answer 1

1)  1 ÷  √2 + √3  = √2 - √3 / 4 - 3
                         =  √2 - √3 / 1
                          = 1.1414 - 1.732
                           = - 0.5906/ -1
                           = 0.5906

2) Consider two triangles Δ  LMP and Δ LNQ         (fig is attached to the answer)
   < MPN  = < NQM ( ALTITUDE AND 90 EACH)
     MN = MN (COMMON)
     MP = QN (GIVEN )

SO Δ LMP ≈ Δ LNQ
      
         LM = LN (CPCT)