[20 - x/√2]/x = 20/10

20 - x/√2 = 2x

20 = x[2 +1/√2]

20√2= x [2√2+1]

x= 20√2/[1+2√2]

The radius of base of a solid cylinder is 7 cm and its height
is 21 cm. It is melted and converted into small bullets.
Each bullet is of same size. Each bullet consisted of two
parts viz. a cylinder and a hemisphere on one of its base.
The total height of bullet is 3.5 cm and radius of base is 2.1
cm. Approximately how many complete bullets can be
obtained?

7*7*21/(2.1*2.1*2.8
.
250/3 = 83 ??

49*21 = n( 2.1² *1.4 + 2/3 *2.1³)
490/2.1 = n( 2.8)
1000/12 =n
83 = n

Let the equal sides are a
Unequal side b
Perimeter 200
2a+b=200

Triangles inequality
2a>b
Put b from the above
2a>200-2a
A>50
A Will be maximum integer at b=2
2a=200-2
A=99
So 50<a<99
49 values

An equliteral triangle inscribed in a rectangle

Remember ,a useful result when this equliteral triangle inscribed in a square it always inclines at 75° with side {√6-√2}x

A right angle ,a square inside, radius of same colour are same find the relationship Between the radius of these circles.

Also prove that
Area of triangle AEF=a quadliratial EFGH

A very useful and important results