Question

wy is a midsegment of △uvx. if uv = p + 57 and wy = 2p + 27, what is the value of p? v w x y u p =

Explanation:

Step1: Apply midsegment theorem

The midsegment of a triangle is half the length of the parallel side, so $WY = \frac{1}{2}UV$.
Substitute the given expressions:
$2p + 27 = \frac{1}{2}(p + 57)$

Step2: Eliminate the fraction

Multiply both sides by 2 to clear the denominator:
$2(2p + 27) = p + 57$
$4p + 54 = p + 57$

Step3: Isolate the variable p

Subtract $p$ and 54 from both sides:
$4p - p = 57 - 54$
$3p = 3$

Step4: Solve for p

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

Answer:

$p = 1$