Question

5 if $\triangle pqr \sim \triangle fgh$, find $qr$.
(there are two triangle figures, one with vertices h, f, g: hf = 4, fg = 6, hg = 6x + 2; the other with vertices q, p, r: qp = 3, pr = 2, qr = x + 3)
a) 1 go to station 10
b) 2 go to station 9
c) 5 go to station 2
d) 3 go to station 3
e) 4 go to station 11

Explanation:

Step1: Set up similarity proportion

Corresponding sides of similar triangles are proportional: $\frac{PQ}{FG} = \frac{QR}{FH}$

Step2: Substitute side values

$\frac{3}{6} = \frac{x+3}{4}$

Step3: Simplify left fraction

$\frac{1}{2} = \frac{x+3}{4}$

Step4: Solve for $x$

Cross multiply: $1 \times 4 = 2(x+3)$
$4 = 2x + 6$
$2x = 4 - 6$
$2x = -2$
$x = -1$

Step5: Calculate $QR$

Substitute $x=-1$ into $QR=x+3$: $QR = -1 + 3$

Answer:

c) 5