Plzz plzz find the value of a that satisfies the congruency of the triangles. in two or more complete sentences, explain the relevance between the congruency of the triangles and the calculations made in finding the value of a

a=√2

Step-by-step explanation:

Given : ΔEGF ≅ ΔHKJ

where ∠G=∠K [right angle]

∠E=∠H=45°

And ∠F=180°-∠E-∠G [By angle sum property]

⇒∠F=180°-45°-90°

⇒∠F=45°=∠J  [corresponding parts of two congruent triangles are congruent]

⇒ Both triangles are isosceles right triangles such that

JK=HK=b , EG=GF

and EF=JH

Now JK=HK= EG=GF=3√2

Now GF=3a=3√2

⇒a=√2

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

17.08

correct me if i am wrong.