HCl Geometry Quiz-2

(C)
as L*B=10000 ie for square L=B=100m
THEN,
IF A RECTANGULAR ADDITIONALLY WAS BUILT ALONG ONE ENTIRE SIDE IT ENSURES THAT ONE SIDE MUST BE REMAIN SAME AS THE SQUARE
HENCE EQUATION BECOMES
(100+X)100=10000+(1/2)*10000
(100+X)100=15000
X=50

let radius of inner circle=r1
radius of outer circle=r2
Also r1=1/3*r2
3*r1=r2
circumference of inner circle=2*pi*r1
circumference of outer circle=2*pi*r2
=6*pi*r1 (since r2=3*r1)
2*pi*r1 + 6*pi*r1 =88 (as per question)
r1=3.5 m
r2=3*3.5
=10.5 m
width of road =10.5 - 3.5 =7 m Ans.

I'm going to guess that the grain is on the ground.
Then the distance each bird flies is the hypotenuse formed by the triangle
with one leg their building and the other the distance to the grain.

Let x = distance grain is from the church, then
350 - x = distance from the Catholic tower

Using the Pythagorean Theorem:
distance the bird on the church flies = √(x^2 + 150^2)
......................................… + 22,500)
distance the bird on the Catholic tower flies = √[(350-x)^2 + 200^2]
......................................… √(122,500 - 700x + x^2 + 40,000)
......................................… √(x^2 - 700x +162,500)

d=r*t, but you said that their rates were constant and they arrived at the same time,
That means whatever faster rate the Catholic bird flew at it was enough to make
the distances seem to be equal.

√(x^2 + 22,500 = √(x^2 - 700x + 162,500)....square both sides to remove radical
x^2 + 22,500 = x^2 - 700x + 162,500............get = to 0 by subtracting the left side
-700x + 140,000 = 0......................................g… x-term alone by subtracting140,000
-700x = -140,000
x = 200 ft is the distance from the church

no. of such cubes = volume of material / volume of one cube
(12*18*6)/(3*3*3)= 48