Question

thursday
a right triangle and two of its side lengths are shown in the diagram.
12 cm
39 cm
x cm
which measurement is closest to the value of x in centimeters?
a 37.1 cm
b 40.8 cm
c 27 cm
d 51 cm

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is hypotenuse, \( a, b \) are legs. Here, hypotenuse \( c = 39 \), one leg \( a = 12 \), another leg \( b = x \). So \( x^2 + 12^2 = 39^2 \).

Step2: Solve for \( x^2 \)

Calculate \( 39^2 - 12^2 \). \( 39^2 = 1521 \), \( 12^2 = 144 \), so \( x^2 = 1521 - 144 = 1377 \).

Step3: Find \( x \)

Take square root: \( x = \sqrt{1377} \approx 37.1 \).

Answer:

A. 37.1 cm