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

Value is x=8 and y=4

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.