Circle c is inscribed in triangle qsu. what is the perimeter of triangle qsu? a. 3units b. 16units c.30 units d. 40 units

d. 40 units

Step-by-step explanation:

(D) 40 units

Step-by-step explanation:

Since Circle C is inscribed in Triangle QSU, the segments connected to the vertex are congruent:

QR = 10  ⇒  QV = 10

UT =  4   ⇒   UV = 4

SR = 2x  ⇒  ST = 2x

It is given that ST = x + 3, and we just determined that ST = 2x, so we can find "x" by solving x + 3 = 2x  ⇒ x = 3

SR = 2x   = 2(3)   = 6  

ST = x + 3   = (3) + 3  = 6

Perimeter = QR + QV  +  SR + ST  + UT + UV

                 =    2(10)     +    2(6)       +   2(4)

                 =     20       +     12         +    8

                 = 40

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