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Answer:
Value is x=8 and y=4
Step-by-step explanation:
Given : A right triangle 'A' hypotenuse length of x+4 and a leg of x,
and right triangle 'B' hypotenuse length of 3y and a leg length of y+4
To find : For what values of x and y are the triangles congruent by HL?
Solution :
Triangle A,
Hypotenuse: x+4
Leg: x
Triangle B,
Hypotenuse: 3y
Leg: y+4
Since the triangle A and B are congruent so, the sides of triangles are equal.
(Hypotenuse are equal) ..........[1]
and (Legs are equal) ..........[2]
Solving the equation of system,
Put the value of x from [2] in [1],
Substitute y in [2],
Therefore, The value of x=8 and y=4
Verifying for the values of x and y:
Triangle A,
Hypotenuse: x+4=8+4=12
Leg: x=8
Triangle B,
Hypotenuse: 3y=3(4)=12
Leg: y+4=4+4=8
Both hypotenuses and both legs are equal hence they are congruent.