Latest Elitmus Aptitude Question SOLUTION: Perimeter of rhombus is equal to perimeter of circle. Longest distance between two points in rhombus is 80. Area of rhombus is 2400 cm^2. Find area of circle. Options: 10000, 6250

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(#M40155204) ELITMUS Category question Keep an EYE

Perimeter of rhombus is equal to perimeter of circle. Longest distance between two points in rhombus is 80. Area of rhombus is 2400 cm^2. Find area of circle.
Options: 10000, 62500, 2500, one more I don't Remember.

Asked In Elitmus JUGAL KHAJURIYA (8 years ago)

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Preetam  (8 years ago)

Let Diagonals of Rhombus are p,q and side is a .

Let Longest side is one of the p and q, let its p=80;

Area of a Rhombus is A =p*q/2
A=2400
2400=80 *q /2
4800=80q=> q=60
4a^2 =60^2 + 80^2
4a^2=10,000=> a=>50

Given: Perimeter of R = Perimeter of Circle

4a = 2*3.14* r=> r=31.84
Area of circle = 3.14* r^2 = 3184.28678
IN Rhombus 4a^2 = p^2 + q^2

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Deepika Anjana  (8 years ago)

all the sides of a rhombus are equal, therefore the perimeter of arhombus would be 4s, and perimeter of a circle = 2pie.r, where r is radius. then acc. to qstn,
4s = 2pie.r........ eq.1
area of a rhombs = 1/2.digonal1.diagonal2
one of the diagonal of rhombus = 80
then acc. to qstn, 1/2.80.d2= 2400
therefore d2= 60.
now diagonals of a rhombus bisects each other at 90 degree. and also divides diagonal into two equal parts. therefore there will be a right angled triangle inside a rhombus, with two sides that will hold the right angle would be 30, and 40,( half of the diagonals). now using the pythagoras triplet, the third side of the triangle would be 50, as well as, it would be the side of rhombus.
now the perimeter of rhombus would be 4s= 4.50= 200. by putting this value in eq. 1, we get 200= 2pie.r
r = 100/pie.
now area of a circle = pie.r^2= pie.(100/pie)^2 = 3183.0988(answer)

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Amitkumar  (8 years ago)

Ans-10000/π

Perimeter of rhombus = perimeter of circle
Let's take perimeter of rhombus = 4a
Length of 1st diagonal d1= 80
Length of 2nd = d2
Area of rhombus = 1/2 * d1*d2
2400= 1/2 * 80*d2
d2=60
a=√(30)^2+(40)^2
a=50
Perimeter=50*4=200
2πr=200
r=100/π
Area of circle=πr^2
=π*(100/π)^2
=10000/π

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Kola Yekanth  (8 years ago)

1/2*h1*h2=2400 given h1=80
=>h2=60
s=sqrt((h1/2)^2 =(h2/2)^2) ==>s=sqrt((40^2)+(30^2))
=>s=50 =>4s=2*pi*r=200
=>r=100/pi =>pi*r^2=10,000/pi

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