In the given figure, seg PA, seg QB, seg RC, and seg SD are perpendicular to line AD. AB = 60, BC = 70, CD = 80, PS = 280 then Find PQ, QR, and RS.

Answer:- 

Given that in the figure, seg PA, seg QB, seg RC, and seg SD are perpendicular to line AD, AB = 60, BC = 70, CD = 80, and PS = 280.

First, we can find the length of line segment AD by adding the lengths of AB, BC, and CD:

AD = AB + BC + CD = 60 + 70 + 80 = 210

We can also use the Intercept theorem to find the lengths of PQ, QR, and RS. The Intercept theorem states that when two parallel lines are intersected by two intersecting lines, the ratios between the corresponding line segments are equal.

So, we have:

PQ/AB = QR/BC = RS/CD = PS/AD

Substituting the given values, we get:

PQ/60 = QR/70 = RS/80 = 280/210

Simplifying, we get:

PQ/60 = 4/3 QR/70 = 4/3 RS/80 = 4/3

Solving for PQ, QR, and RS, we get:

PQ = (4/3)*60 = 80 QR = (4/3)*70 = 280/3 RS = (4/3)*80 = 320/3

Therefore, the length of PQ is 80, the length of QR is 280/3, and the length of RS is 320/3.