Question

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 1

`{:("seg PA, seg QB, seg RC, and seg SD are perpendicular to line AD."),("AB = 60, BC = 70, CD = 80, PS = 280"):} ...}"Given"`

AD = AB + BC + CD

∴ AD = 60 + 70 + 80

∴ AD = 210

The lines PA, QB, RC, and SD are parallel to each other.

The Intercept theorem provides the ratios between the line segments created when two parallel lines are intercepted by two intersecting lines.

By the Intercept Theorem,

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

∴ `"PQ"/60 = "QR"/70 = "RS"/80 = 280/210`

Considering `"PQ"/60 = 280/210`,

∴ `"PQ"/60 = 280/210`

∴ `"PQ" = (280 × 60)/210`

∴ PQ = 80

Considering `"QR"/70 = 280/210`

∴  `"QR"/70 = 280/210`

∴  `"QR" = (280 × 70)/210`

∴  `"QR" = 280/3`

Considering `"RS"/80 = 280/210`

∴ `"RS"/80 = 280/210`

∴ `"RS" = (280 × 80)/210`

∴ `"RS" =320/3`