Question

a right triangle is shown, with dimensions in feet (ft).
x ft
√13 ft 3 ft
what is the value of x?
ⓐ 2
ⓑ 4
ⓒ √22
ⓓ √160

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is hypotenuse, \( a,b \) are legs. Here, \( c = \sqrt{13} \), \( b = 3 \), \( a = x \). So \( x^2 + 3^2 = (\sqrt{13})^2 \).

Step2: Simplify the equation

Calculate \( 3^2 = 9 \), \( (\sqrt{13})^2 = 13 \). Equation becomes \( x^2 + 9 = 13 \).

Step3: Solve for \( x^2 \)

Subtract 9 from both sides: \( x^2 = 13 - 9 = 4 \).

Step4: Solve for \( x \)

Take square root: \( x = \sqrt{4} = 2 \) (since length is positive).

Answer:

A. 2