Answer:
[tex] w = 6 [/tex]
Step-by-step explanation:
ST = w + 6,
PR = w
From the diagram given, we can deduce that PR is the midsegment of ∆QST. Therefore, according to the midsegment theorem:
PR = ½ of ST
Plug in the values into the equation and solve for w.
[tex] w = \frac{1}{2}(w + 6) [/tex]
[tex] w = \frac{w}{2} + 3 [/tex] (distributive property of equality)
[tex] w - 3 = \frac{w}{2} [/tex] (subtraction property of equality)
[tex] 2(w - 3) = \frac{w}{2}*2 [/tex] (multiplication property of equality)
[tex] 2w - 6 = w [/tex]
[tex] 2w - 6 - 2w= w - 2w [/tex] (subtraction property of equality)
[tex] - 6 = - w [/tex]
Divide both sides by -1
[tex] 6 = w [/tex]
[tex] w = 6 [/tex]
