Question

for the triangles to be congruent by hl, what must be the value of x? 7 4 3 2

Explanation:

Step1: Apply HL - Hypotenuse - Leg theorem

For right - triangles to be congruent by HL, the hypotenuses and one pair of legs must be equal. Let's assume the hypotenuse of the first triangle is 15 and the hypotenuse of the second triangle is \(3x + 3\), and a leg of the first triangle is 12 and a leg of the second triangle is \(2x+1\). We can set up the following equations based on the HL theorem. First, set the hypotenuses equal: \(3x + 3=15\).

Step2: Solve the hypotenuse equation for x

Subtract 3 from both sides of the equation \(3x + 3=15\):
\[

$$\begin{align*} 3x+3 - 3&=15 - 3\\ 3x&=12 \end{align*}$$

\]
Then divide both sides by 3: \(x = 4\). We can also check by setting the legs equal: \(2x+1 = 12\). Substitute \(x = 4\) into \(2x + 1\), we get \(2\times4+1=8 + 1=9
eq12\). But if we set the hypotenuse \(3x + 3 = 15\) and solve for \(x\), we have:
\[

$$\begin{align*} 3x+3&=15\\ 3x&=12\\ x&=4 \end{align*}$$

\]

Answer:

4