Each side of an equilateral triangle is incre | vedclass

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

Question

(C) Let the original side of the equilateral triangle be $a$.The original area $A = \frac{\sqrt{3}}{4} a^2$.The new side length $a' = a + 1.5\% 	ext{

Vedclass · Accepted Answer

$3.0225$

Vedclass · Answer

(C) Let the original side of the equilateral triangle be $a$.The original area $A = \frac{\sqrt{3}}{4} a^2$.The new side length $a' = a + 1.5\% 	ext{ of } a = a(1 + 0.015) = 1.015a$.The new area $A' = \frac{\sqrt{3}}{4} (a')^2 = \frac{\sqrt{3}}{4} (1.015a)^2 = \frac{\sqrt{3}}{4} a^2 (1.015)^2$.Since $A' = A 	imes (1.015)^2$,we calculate $(1.015)^2 = 1.030225$.So,$A' = 1.030225 A$.The percentage increase in area $= \frac{A' - A}{A} 	imes 100 = (1.030225 - 1) 	imes 100 = 0.030225 	imes 100 = 3.0225 \%.$

Each side of an equilateral triangle is increased by $1.5 \%$. The percentage increase in its area is......$\%$

Similar Questions

$A$ hollow spherical shell is made of a metal of density $4.9 \, g/cm^3$. If its internal and external radii are $10 \, cm$ and $12 \, cm$ respectively,find the weight of the shell. (Take $\pi = 3.1416$) (in $gm$)

The perimeter of an equilateral triangle is $72 \sqrt{3} \text{ cm}$. Find its height in meters.

$3$ horses are tethered at $3$ corners of a triangular plot of land having sides $20 \, m$,$30 \, m$,and $40 \, m$,each with a rope of length $7 \, m$. The area (in $m^2$) of the region of this plot,which can be grazed by the horses,is (Use $\pi = \frac{22}{7}$)

If a diagonal of a square is doubled,how does the area of the square change?

Given that the volume of a metal sphere is $38808 \, cm^{3}$. Then,its radius and its surface area are?

Vedclass Test Series

Exam Paper Generator

Online Exam Module