The areas of two equilateral triangles are in the ratio 25 : 36. Their altitudes will be in the ratio :
A. 25 : 36
B. 36 : 25
C. 5 : 6
D. $$\sqrt 5 $$ : $$\sqrt 6 $$
Answer: Option C
Solution(By Examveda Team)
Let the length of sides of the two triangles be a1 and a2 respectively and their altitudes be h1 and h2 respectively.Then,
$$\eqalign{ & \Leftrightarrow \frac{{\frac{{\sqrt 3 }}{4}a_1^2}}{{\frac{{\sqrt 3 }}{4}a_2^2}} = \frac{{25}}{{36}} \cr & \Rightarrow {\left( {\frac{{{a_1}}}{{{a_2}}}} \right)^2} = {\left( {\frac{5}{6}} \right)^2} \cr & \Rightarrow \frac{{{a_1}}}{{{a_2}}} = \frac{5}{6} \cr} $$
And
$$\eqalign{ & \Leftrightarrow \frac{{\frac{1}{2} \times {a_1} \times {h_1}}}{{\frac{1}{2} \times {a_2} \times {h_2}}} = \frac{{25}}{{36}} \cr & \Rightarrow \frac{5}{6} \times \frac{{{h_1}}}{{{h_2}}} = \frac{{25}}{{36}} \cr & \Rightarrow \frac{{{h_1}}}{{{h_2}}} = \frac{{25}}{{36}} \times \frac{6}{5} \cr & \Rightarrow \frac{{{h_1}}}{{{h_2}}} = \frac{5}{6} \cr} $$
Related Questions on Area
A. 15360 m2
B. 153600 m2
C. 30720 m2
D. 307200 m2
E. None of these
A. 2%
B. 2.02%
C. 4%
D. 4.04%
E. None of these
A. 16 cm
B. 18 cm
C. 24 cm
D. Data inadequate
E. None of these
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A. 40%
B. 42%
C. 44%
D. 46%
Join The Discussion