Question

Given right triangle A w/a hypotenuse length of x+4 and a leg of x, and right triangle B, w/ a hypotense length of 3y and a leg length of y+4 for what values of x and y are the triangles congruent by HL?

Answer 1

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.

$x+4=3y$    (Hypotenuse are equal)  ..........[1]

and $x=y+4$   (Legs are equal)   ..........[2]

Solving the equation of system,

Put the value of x from [2] in [1],

$x+4=3y$

$y+4+4=3y$

$8=2y$

$y=4$

Substitute y in [2],

$x=y+4$

$x=4+4$

$x=8$

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.