Question

of the variable(s).

1. x = 6

right triangle with vertical leg labeled ( x ), horizontal leg labeled ( 4x + 1 ), and a right angle symbol at their intersection

Explanation:

Assuming we need to find the lengths of the legs (or maybe area, but since it's a right triangle with legs \( x \) and \( 4x + 1 \), and \( x = 6 \)):

Step 1: Substitute \( x = 6 \) into \( 4x + 1 \)

To find the length of the horizontal leg, substitute \( x = 6 \) into the expression \( 4x + 1 \).
\( 4(6) + 1 = 24 + 1 = 25 \)

Step 2: Identify the lengths of the legs

The vertical leg is \( x = 6 \), and the horizontal leg is \( 4x + 1 = 25 \) (from Step 1). If we were to find the area (though not specified, but common in right triangles), the area \( A \) of a right triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \).

Step 3: Calculate the area (if needed)

Using base \( = 25 \) and height \( = 6 \),
\( A = \frac{1}{2} \times 25 \times 6 = \frac{150}{2} = 75 \)

(If the problem was just to find the lengths, then the vertical leg is 6 and horizontal is 25. If area, then 75. Since the original problem's text is cut off, but given \( x = 6 \), let's assume finding the lengths of the legs and maybe area. Let's check the common problem type here: right triangle with legs \( x \) and \( 4x + 1 \), \( x = 6 \), so lengths are 6 and 25, area 75.)

Answer:

If finding the lengths: Vertical leg \( x = 6 \), Horizontal leg \( 4x + 1 = 25 \). If finding the area: \( 75 \). (Assuming area, the answer is \( \boldsymbol{75} \))