Question

if $sw = p - 16$ and $tv = -p + 52$, what is the value of $p$?
$p = \square$

Explanation:

Step1: Identify segment relationship

From the triangle markings, $TV$ is the midsegment of $\triangle USW$, so $TV = \frac{1}{2}SW$.

Step2: Substitute given expressions

Substitute $SW = p - 16$ and $TV = -p + 52$ into the midsegment formula:
$$-p + 52 = \frac{1}{2}(p - 16)$$

Step3: Eliminate the fraction

Multiply both sides by 2 to clear the denominator:
$$2(-p + 52) = p - 16$$
$$-2p + 104 = p - 16$$

Step4: Isolate the variable $p$

Combine like terms by adding $2p$ to both sides and adding 16 to both sides:
$$104 + 16 = p + 2p$$
$$120 = 3p$$

Step5: Solve for $p$

Divide both sides by 3:
$$p = \frac{120}{3}$$

Answer:

$p = 40$