Given a right triangle where $tv$ = $24$ and $xz$ = $13$, what is the value of $vw-yz$?

• A. $24$
• B. $11$
• C. $1$
• D. $37$

Answer: (B)

Verified step by step guidance

1. Identify the sides of the right triangle given: \( tv = 24 \) and \( xz = 13 \). These likely represent lengths of two sides of the triangle.
2. Recall the Pythagorean theorem for a right triangle: \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse and \( a \), \( b \) are the legs.
3. Determine which sides correspond to the legs and which is the hypotenuse. Since 13 is smaller than 24, it is likely that 13 and 24 are legs or one is the hypotenuse. Check if \( 24^2 + 13^2 \) or \( 24^2 - 13^2 \) fits the Pythagorean theorem.
4. Calculate the missing side \( vw - yz \) by expressing it in terms of the known sides and applying the Pythagorean theorem accordingly.
5. Write the expression for \( vw - yz \) and simplify it using the values of the sides and the Pythagorean relationship to find the length.