Answer:
1) Length QR is 8 units
2) The T shirt stand should be placed at the circumcenter of the Three points
of triangle formed
3) Length FB is 21 units
Step-by-step explanation:1
1) In triangle PSQ and RSQ,
[tex]PS = SR[/tex], ∠PSQ = ∠RSQ and SQ is common side.
Thus, the two triangles are congruent.
Thus, sides PQ = RQ
[tex]3n-1 = 5n-7[/tex]
n = 3.
Thus, QR = 5(n) - 7 = 5(3) - 7 = 15 - 7 = 8 units.
2) A point inside the triangle which is equidistant from all 3 points is a circumcenter, Thus T-shirt stand to be placed at the circumcenter of triangle.
3) In triangle CBF and CDF,
[tex]∠BCF = ∠DCF[/tex], ∠CDF = ∠CBF and CF is common side.
Thus, the two triangles are congruent.
Thus, sides FD = BF
[tex]6x+3= 4x+9[/tex]
x = 3.
Thus, FB = 6(x) + 3 =6(3) + 3 = 18 + 3 = 21 units.
