Answer:
a=√2
Step-by-step explanation:
Given that ΔEGF and ΔHKJ are congruent.
So, first writing the congruency of the triangle
As ∠E=∠H=45° and ∠G=∠K=90°
Corresponding angles of ∠E and ∠G are ∠H and ∠K respectively.
Therefore, ΔEGF ≅ ΔHKJ
As the corresponding parts of the congruent triangles are equal
So, EG=HK, GF=KJ
, and EF=HJ.
From the figure, GF=3a, and KJ=b
So, 3a=b
Therefore, a=3/b...(i)
Similarly, from the figure, EF=6, and HJ=b√2
So, b√2=6
Therefore, b=6/√2=3√2...(ii)
Putting the value of b from equation (ii) to equation (i), we have,
a=3/(3√2)=√2
Hence, the value of a is √2.
