Question

rt is a midsegment of △pqs. if pq = x and rt = x - 47, what is the value of x? triangle image with vertices q, p, s, midsegment rt

Explanation:

Step1: Apply the midsegment theorem

The midsegment theorem states that the length of a midsegment of a triangle is half the length of the side it is parallel to. So, \( PQ = 2RT \).

Step2: Substitute the given expressions

Given \( PQ=x \) and \( RT = x - 47 \), substitute into the equation \( x=2(x - 47) \).

Step3: Solve the equation

Expand the right - hand side: \( x=2x-94 \).
Subtract \( x \) from both sides: \( 0=2x - x-94 \).
Simplify to get \( x = 94 \).

Answer:

\(94\)