Question

gilberts family is building a walkway between the second floor balcony on his house and his tree house. how long will the walkway be?

Explanation:

Step1: Apply the Pythagorean theorem

Let the length of the walkway be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 30\), \(c=50\), and \(b=x\).
So, \(30^{2}+x^{2}=50^{2}\).

Step2: Simplify the equation

\(900+x^{2}=2500\).
Subtract \(900\) from both sides: \(x^{2}=2500 - 900\).
\(x^{2}=1600\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{1600}\).
\(x = 40\).

Answer:

\(40\) feet.