Question

which value of x would make △suv≅△tuw by hl? 2 3 4 5

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

For right - triangles $\triangle SUV$ and $\triangle TUW$, if $\triangle SUV\cong\triangle TUW$ by HL, then the hypotenuses are equal. So, $SV = TW$.
We have $SV=2x + 9$ and $TW = 4x-1$.
Set up the equation: $2x + 9=4x - 1$.

Step2: Solve the equation for x

First, subtract $2x$ from both sides of the equation:
$2x+9-2x=4x - 1-2x$.
This simplifies to $9 = 2x-1$.
Then, add 1 to both sides: $9 + 1=2x-1 + 1$, which gives $10 = 2x$.
Finally, divide both sides by 2: $\frac{10}{2}=\frac{2x}{2}$, so $x = 5$.

Answer:

5