Question

In adjoining figure $PQ\perp BC,$ $AD\perp BC$ then find following ratios.

(i) $\frac{A△PQB}{A△PBC}$ [A represents Area]
(ii) $\frac{A△PBC}{A△ABC}$
(iii) $\frac{A△ABC}{A△ADC}$
(iv) $\frac{A△ADC}{A△PQC}$

Answer 1

Area of triangle $=\frac{1}{2}\times$ base $\times$ height

(i) $\frac{A△PQB}{A△PBC}=\frac{\frac{1}{2}\times PQ\times BQ}{\frac{1}{2}\times PQ\times BC}=\frac{BQ}{BC}$

(ii) $\frac{A△PBC}{A△ABC}=\frac{\frac{1}{2}\times PQ\times BC}{\frac{1}{2}\times AD\times BC}=\frac{PQ}{AD}$

(iii) $\frac{A△ABC}{A△ADC}=\frac{\frac{1}{2}\times AD\times BC}{\frac{1}{2}\times AD\times DC}=\frac{BC}{DC}$

(iv) $\frac{A△ADC}{A△PQC}=\frac{\frac{1}{2}\times AD\times DC}{\frac{1}{2}\times PQ\times QC}=\frac{AD\times DC}{PQ\times QC}$