In ΔABC ∠A = 90° and AD ⊥ BC where D lies on BC. If BC = 8 cm, AD = 6 cm, then arΔABC : arΔACD = ?
A. 4 : 3
B. 25 : 16
C. 16 : 9
D. 25 : 9
Answer: Option C
Solution(By Examveda Team)
According to question,ΔABC ∼ ΔACD
$$\eqalign{ & \therefore \frac{{{\text{area}}\,{\text{of}}\,\Delta ABC}}{{{\text{area}}\,{\text{of}}\,\Delta ACD}} = \frac{{B{C^2}}}{{A{D^2}}} \cr & \frac{{{\text{area}}\,{\text{of}}\,\Delta ABC}}{{{\text{area}}\,{\text{of}}\,\Delta ACD}} = \frac{{{8^2}}}{{{6^2}}} \cr & \frac{{{\text{area}}\,{\text{of}}\,\Delta ABC}}{{{\text{area}}\,{\text{of}}\,\Delta ACD}} = \frac{{64}}{{36}} \cr & \frac{{{\text{area}}\,{\text{of}}\,\Delta ABC}}{{{\text{area}}\,{\text{of}}\,\Delta ACD}} = \frac{{16}}{9} \cr} $$
area ΔABC : area ΔACD = 16 : 9
Related Questions on Triangles
If ABC and PQR are similar triangles in which ∠A = 47° and ∠Q = 83°, then ∠C is:
A. 50°
B. 70°
C. 60°
D. 80°
In the following figure which of the following statements is true?
A. AB = BD
B. AC = CD
C. BC + CD
D. AD < Cd
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