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

Two circles touch internally. The sum of their areas is $116\, \pi \, cm^2$ and the distance between their centers is $6 \, cm$. Then,the radii of the circles are?

The length of a rectangular plot is $60\%$ more than its breadth. If the difference between the length and the breadth of that rectangle is $24\, cm$,what is the area of that rectangle? (in $cm^2$)

What will be the cost of gardening a $1 \text{ m}$ broad boundary around a rectangular plot having a perimeter of $340 \text{ m}$ at the rate of $₹ 10$ per square metre?

The area of a sector of a circle of radius $5 \, cm$,formed by an arc of length $3.5 \, cm$,is ..... $cm^2$.

The least number of square slabs that can be fitted in a room of $10.5 \text{ m}$ long and $3 \text{ m}$ wide is........?

Vedclass Test Series

Exam Paper Generator

Online Exam Module