Question

the triangle shown below has an area of 18 units². 6 x find the missing length. x = units

Explanation:

Step1: Recall area formula for right triangle

The area \( A \) of a right triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Here, the legs of the right triangle are 6 (one leg) and \( x \) (the other leg), so base = 6, height = \( x \), and \( A = 18 \).

Step2: Substitute values into formula

Substitute \( A = 18 \), base = 6, and height = \( x \) into the formula: \( 18 = \frac{1}{2} \times 6 \times x \).

Step3: Simplify and solve for \( x \)

First, simplify \( \frac{1}{2} \times 6 = 3 \), so the equation becomes \( 18 = 3x \). Then, divide both sides by 3: \( x = \frac{18}{3} = 6 \).

Answer:

6