On decreasing each side of an equilateral tri | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The area of an equilateral triangle with side $a$ is given by $A = \frac{\sqrt{3}}{4} a^2$.When each side is decreased by $2\, cm$,the new side be

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) The area of an equilateral triangle with side $a$ is given by $A = \frac{\sqrt{3}}{4} a^2$.When each side is decreased by $2\, cm$,the new side becomes $(a - 2)$.The new area is $A' = \frac{\sqrt{3}}{4} (a - 2)^2$.According to the problem,the decrease in area is $4\sqrt{3}\, cm^2$,so $A - A' = 4\sqrt{3}$.$\frac{\sqrt{3}}{4} a^2 - \frac{\sqrt{3}}{4} (a - 2)^2 = 4\sqrt{3}$.Dividing both sides by $\frac{\sqrt{3}}{4}$,we get $a^2 - (a - 2)^2 = 16$.Expanding the square: $a^2 - (a^2 - 4a + 4) = 16$.$a^2 - a^2 + 4a - 4 = 16$.$4a - 4 = 16$.$4a = 20$.$a = 5\, cm$.

On decreasing each side of an equilateral triangle by $2\, cm$,there is a decrease of $4\sqrt{3}\, cm^2$ in its area. The length of each side of the triangle is.........$cm$.

Similar Questions

If in a triangle,the area is numerically equal to the perimeter,then the radius of the inscribed circle of the triangle is

$A$ parallelogram has sides $60\, cm$ and $40\, cm$ and one of its diagonals is $80\, cm$ long. Its area is

The area of a square is $1444 \ m^2$. The breadth of a rectangle is $\frac{1}{4}$ of the side of the square and the length of the rectangle is thrice its breadth. What is the difference between the area of the square and the area of the rectangle? (in $m^2$)

$A$ circular disc of area $0.49 \pi \, m^2$ rolls down a length of $1.76 \, km$. The number of revolutions it makes is:

The perimeter of an isosceles triangle is $14 \ cm$. The lateral side and the base are in the ratio $5:4$. The area of the triangle in $cm^2$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module