Let the length be 'l' and breadth be 'b'.

b = l × 3/4__________(a)

2(l+b) = 1050

l+b = 525___________(b)

From equations (a) and (b),

l = 300m, b = 225 m

Area = l × b

= 300 × 225

= 67500 sq.m.

Let length, breadth and height of the room be 7, 3, 1 unit respectively.

Area of walls = 2(l+b)xh = 2(7+3)x1 = 20 sq. unit.

Now, length, breadth and height of room will become 3.5, 6 and 2 respectively. 

Area of walls = 2(l+b)xh = 2(3.5+6)x2 = 38 sq. unit. 

% Increase in the area of walls = (38-20)x100/20 = 90%.

Number of square units in 13 by 9 is given by the area it forms with length and breadth as 13 & 9

Area = 13 x 9 = 117

Hence, number of square units in 13 by 9 is 117 sq.units.

Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then,  1 2 × x × 3 h 1 2 × y × 4 h = 4 3 ? x y = 4 3 × 4 3 = 16 9 

Required ratio = 16 : 9.

Area = (13.86 x 10000) sq.m = 138600 sq.m

?R 2 = 138600 ? R 2 = 138600 × 7 22 ? R = 210 m 

Circumference =  2 ?R 2 = 2 × 22 7 × 210 = 1320 m 

Cost of fencing = Rs. (1320 x 4.40) = Rs. 5808.

perimeter of window = ?r+2r 

= [(22/7) x (63/2) + 63] = 99+63 = 162 cm

Let the triangle and parallelogram have common base b, 

let the Altitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then  

Area of triangle    =  1 2 × b × h 1 

Area of rectangle  = b*h2 

As per Given,

1 2 * b * h 1 = b * h 2

1 2 * b * h 1 = b * 100

 h1=200

We know that, 

The area of a triangle with two sides given and included angle

A = 1/2 x product of sides x Sin(angle) 

Here the two sides are 8 & 12

Angle = 150

Area = 1/2 x 8 x 12 x sin150

Sin(150) = sin(90+60) = cos(60) = 1/2

A = 48 x 1/2 = 24

Area of the given triangle = 24 sq units.

?r = 66 7

 r =3

l=5.5m w=3.75m
area of the floor = 5.5 x 3.75 = 20.625 sq m
cost of paving = 800 x 20.625 = Rs. 16500