Question

a right triangle and two of its side lengths are shown in the diagram. 64 cm w cm 6 cm which measurement is closest to the value of w? 63.7 cm 32 cm 64.3 cm 254.9 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, \( c = 64 \), \( b = 6 \), find \( a = W \). So \( W^2 + 6^2 = 64^2 \).

Step2: Solve for \( W^2 \)

\( W^2 = 64^2 - 6^2 = (64 - 6)(64 + 6) = 58\times70 = 4060 \) (using difference of squares: \( a^2 - b^2=(a - b)(a + b) \))

Step3: Calculate \( W \)

\( W=\sqrt{4060}\approx63.7 \) (since \( 63.7^2\approx4057.69 \), close to 4060)

Answer:

63.7 cm