Question

use a pythagorean triple to find x.
right triangle with legs 28 and 96, hypotenuse x
x = \boxed{}

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are legs, \( c \) is hypotenuse. Here, \( a = 28 \), \( b = 96 \), \( c = x \).

Step2: Factor out common terms

Notice 28 and 96 are multiples of 4: \( 28 = 4 \times 7 \), \( 96 = 4 \times 24 \). So \( x^2=(4\times7)^2+(4\times24)^2 = 16\times(7^2 + 24^2) \).

Step3: Calculate \( 7^2 + 24^2 \)

\( 7^2 = 49 \), \( 24^2 = 576 \), so \( 49 + 576 = 625 \).

Step4: Simplify \( x^2 \)

\( x^2 = 16\times625 = 10000 \).

Step5: Find \( x \)

Take square root: \( x = \sqrt{10000} = 100 \).

Answer:

100