Question

in the given right triangle, find the side labeled x. x = box (right triangle with leg 24, leg x, hypotenuse x+2)

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( a = 24 \), \( b = x \), \( c = x + 2 \). So \( 24^2 + x^2=(x + 2)^2 \).

Step2: Expand and simplify

Expand \( (x + 2)^2 \) to \( x^2 + 4x + 4 \). Then \( 576+x^2=x^2 + 4x + 4 \). Subtract \( x^2 \) from both sides: \( 576 = 4x + 4 \).

Step3: Solve for x

Subtract 4: \( 572 = 4x \). Divide by 4: \( x=\frac{572}{4}=143 \).

Answer:

143