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

Given:
AB = 60,
BC = 70,
CD = 80,
PS = 280
Now, AD = AB + BC + CD
= 60 + 70 + 80
= 210
By intercept theorem, we have
$$\begin{gathered} \frac{\mathrm{PQ}}{\mathrm{AB}}=\frac{\mathrm{QR}}{\mathrm{BC}}=\frac{\mathrm{RS}}{\mathrm{CD}}=\frac{\mathrm{PS}}{\mathrm{AD}} \\ \Rightarrow \frac{{\displaystyle \mathrm{PQ}}}{{\displaystyle 60}}=\frac{{\displaystyle \mathrm{QR}}}{{\displaystyle 70}}=\frac{{\displaystyle \mathrm{RS}}}{{\displaystyle 80}}=\frac{{\displaystyle 280}}{{\displaystyle 210}} \\ \Rightarrow \frac{{\displaystyle \mathrm{PQ}}}{{\displaystyle 60}}=\frac{{\displaystyle \mathrm{QR}}}{{\displaystyle 70}}=\frac{{\displaystyle \mathrm{RS}}}{{\displaystyle 80}}=\frac{{\displaystyle 4}}{{\displaystyle 3}} \end{gathered}$$
$$\begin{gathered} \therefore \mathrm{PQ}=\frac{{\displaystyle 4}}{{\displaystyle 3}}\times 60=80 \\ \mathrm{QR}=\frac{{\displaystyle 4}}{{\displaystyle 3}}\times 70=\frac{280}{3} \\ \mathrm{RS}=\frac{{\displaystyle 4}}{{\displaystyle 3}}\times 80=\frac{320}{3} \end{gathered}$$