Questions: Find the length of ×

△ Find the length of \( x \) in a right-angled triangle given one leg and the hypotenuse. ○ Apply the Pythagorean theorem ▷ Use the Pythagorean theorem to relate the squares of the sides of the triangle. ☼ The Pythagorean theorem states \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. Substituting the given values: \( 3^2 + x^2 = 7^2 \). ○ Simplify the equation ▷ Simplify the squares and isolate \( x^2 \). ☼ Calculating: \( 9 + x^2 = 49 \). Subtracting 9 from both sides gives \( x^2 = 40 \). ○ Solve for \( x \) ▷ Take the square root of both sides to find \( x \). ☼ \( x = \sqrt{40} = \sqrt{4 \cdot 10} = 2\sqrt{10} \). Thus, the length of \( x \) is \( 2\sqrt{10} \). ✧ The length of \( x \) is \( 2\sqrt{10} \). ☺ x = 2√10