Question

Please help asap!!!

Answer 1

Answer:

$w = 6$

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.

$w = \frac{1}{2}(w + 6)$

$w = \frac{w}{2} + 3$ (distributive property of equality)

$w - 3 = \frac{w}{2}$ (subtraction property of equality)

$2(w - 3) = \frac{w}{2}*2$ (multiplication property of equality)

$2w - 6 = w$

$2w - 6 - 2w= w - 2w$ (subtraction property of equality)

$- 6 = - w$

Divide both sides by -1

$6 = w$

$w = 6$