Question

b. solve for p in the figure.
t
s
p
p
t=12
s

Explanation:

To solve for \( p \) in the given triangle, we assume it is an isosceles right triangle (since sides \( TP \) and \( TS \) are labeled with \( s \) and \( p \), and side \( SP = t = 12 \)). In an isosceles right triangle, the legs are equal, and the hypotenuse \( c \) is related to the leg \( a \) by \( c = a\sqrt{2} \). Here, if \( SP \) is the hypotenuse, then:

Step 1: Identify the relationship

For an isosceles right triangle with leg length \( p \) and hypotenuse \( t = 12 \), the formula is \( t = p\sqrt{2} \).

Step 2: Solve for \( p \)

Rearrange the formula to solve for \( p \):
\( p = \frac{t}{\sqrt{2}} \)

Substitute \( t = 12 \):
\( p = \frac{12}{\sqrt{2}} \)

Rationalize the denominator:
\( p = \frac{12\sqrt{2}}{2} = 6\sqrt{2} \approx 8.485 \)

Answer:

\( p = 6\sqrt{2} \) (or approximately \( 8.49 \))