Question

identifying a leg length
what is the length of \\(\overline{pr}\\)?
\\(\square\\) units
(there is a triangle pqr with angles at p and q marked equal, side pr labeled \\(5n\\) and side qr labeled \\(32 + n\\))

Explanation:

Step1: Recognize isosceles triangle property

The marked angles at P and Q are equal, so the sides opposite them are equal: $5n = 32 + n$

Step2: Solve for n

Subtract $n$ from both sides:
$5n - n = 32 + n - n$
$4n = 32$
Divide both sides by 4:
$n = \frac{32}{4} = 8$

Step3: Calculate length of $\overline{PR}$

Substitute $n=8$ into $5n$:
$5 \times 8 = 40$

Answer:

40 units