Question

Can someone please answer these for me. this is my second time asking

Answer 1

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,

`PS = SR`, ∠PSQ = ∠RSQ and SQ is common side.

Thus, the two triangles are congruent.

Thus, sides PQ = RQ

`3n-1 = 5n-7`

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,

`∠BCF = ∠DCF`, ∠CDF = ∠CBF and CF is common side.

Thus, the two triangles are congruent.

Thus, sides FD = BF

`6x+3= 4x+9`

x = 3.

Thus, FB = 6(x) + 3 =6(3) + 3 = 18 + 3 = 21 units.