Question

Which value of x would make Triangle S U V Is-congruent-to Triangle T U M by HL?

Answer 1

Answer:

$x=5$

Step-by-step explanation:

Actually, the complete question includes the expression of each hypothenuse, because the problem is about congruence between right triangle.

So, the hypothenuse for $\triangle SUV$ is: $2x+9$.

The hypothenuse for $\triangle TUW$ is:   $4x-1$.

So, the postulate HL (Hypothenuse-Leg) states that both right triangles are equal if their hypothenuses and legs are equal. So, we have to make equal both hypothenuse expression and solve for $x$:

$2x+9=4x-1\\9+1=4x-2x\\10=2x\\x=\frac{10}{2}=5$

Therefore, when $x=5$ these triangles are congruent.

Answer 2

Answer:

5

Step-by-step explanation:

2x + 9 = 4x -1

1. substract the 2x from both sides so you end up with 4x - 2x = 2x

2. add the one to both sides so 9+1= 10

3. then divide 10 and 2x = 5