If an equilateral triangle of area X and a square of area Y have the same perimeter, then X is :
A. equal to Y
B. greater than Y
C. less than Y
D. less than or equal to Y
Answer: Option C
Solution(By Examveda Team)
Let the side of the triangle be a cm and each side of the square be b cmThen,
$$\eqalign{ & X = \frac{{\sqrt 3 }}{4}{a^2}{\text{ and }}Y = {b^2} \cr & {\text{Where }}3a = 4b,i,e.,b = \frac{{3a}}{4} \cr} $$
$$\therefore X = \frac{{\sqrt 3 {a^2}}}{4}{\text{ and }}Y = \frac{{9{a^2}}}{{16}}$$ $$\left[ {\because b = \frac{{3a}}{4}} \right]$$
$$\eqalign{ & {\text{Now,}} \cr & \frac{{\sqrt 3 {a^2}}}{4} = \frac{{1.732{a^2}}}{4} = 0.433{a^2} \cr & {\text{And }}\frac{{9{a^2}}}{{16}} = 0.5625{a^2} \cr & \therefore X < Y \cr} $$
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%
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