(i)In rectangle, Perimeter = 14m
Length = 4m
Breadth =?
P = 2(I + b)
14 = 2(4 + b)
14 = 8 + 2b
14 - 8 = 2b
\(6=2b\Rightarrow b=\cfrac { 6 }{ 2 } =3\)
\(\therefore\) Breadth = 3m.
(ii) In isosceles triangle 2 sides are equal.
P = 21 cm, 3^rd side = 5 cm.
P = side 1 + side 2 + side 3
21 = (a + b + c)
21 = (a + a + 5)
\(21a=2a+5\Rightarrow 2a=21-5\)
2a = 16
\(2=\cfrac { 16 }{ 2 } =8\)
\(\therefore\) Equal sides = a = 3 cm, b = 8 cm.

(i)

(ii)
length = 2 (breadth)
I = 2b --------- (1)
Formula: P = 2(1 + b)
= 2 (2b+b) = 2 (3b)
P = 6b units \(\Rightarrow\) P = 6 \(\times\) breadth.
\(\therefore\) Perimeter of a rectangle.
(iii) Side is reduced to half.
\(a=\left( a-\cfrac { a }{ 2 } \right) =\left( \cfrac { 2a-a }{ 2 } \right) =\cfrac { a }{ 2 } \)
 \(\therefore\) Perimeter of a square = 4a
=\(4\left( \cfrac { a }{ 2 } \right) \)
P = 3a units
(iv) All sides are equal in length a = b = c
\(\therefore\) Perimeter of a triangle= ( a + b + c) units
= a + a + a = 3a
\(\therefore\) P = 3a units.

A square of side = 2 cm
A rectangle of length = 15 cm
and
breadth= 10 cm
Perimeter of the combined shape = Perimeter of square + Perimeter of rectangle.

Perimeter of the combined shape = 10 cm + 15 cm + 10 cm + 2 cm + 2 cm + 2 cm + 13 cm
\(\therefore\)  P = 54 cm.

base (b) = 25 m and height (h) = 20 m
Area (A) = \(\left( \cfrac { 1 }{ 2 } \times base\times height \right) \)sq.units
= \(\cfrac { 1 }{ 2 } \times 25\times 20\)
A = 250 m²
A = 250m²
1 sq. m = Rs. 45 
250 sq. m = 45 \(\times\) 250
\(\therefore\)Cost ofthe field = Rs. 11, 250

Perimeter = 40 cm
Two sides are 13 cm and 15 cm
To find: 3^rd side (c)
a + b + C = 40 \(\Rightarrow\) 13 + 15 + c = 40
\(\Rightarrow\) 28 +c = 40
c = 40 - 28 = 12cm
\(\therefore\) Third side = 12 cm

Perimeter (P) = 40 m
Side (8) =?
Area (A) =?
4S = P
\(4S=40\Rightarrow S=\cfrac { 40 }{ 4 } =10m\)
A = S² = 10² = 100m²
\(\therefore\) Side (S) = 10 m, Area (A) = 100 m²

Area of a rectangle = 820 sq. cm
Width (b) = 20 cm
Length (l) =?
Perimeter =?
\(I=\cfrac { A }{ b } \)
= \(\cfrac { 820 }{ 20 } =41\\ \)
= =2(41+20)
= 2 (61) = 122 cm
\(\therefore\) I = 41 cm , P = 122 cm

Sides are = 6 feet, 8 feet and 10 feet
Perimeter = ( a + b + c) feet
= (6+8+10) = 24 feet.
Area = \(\cfrac { 1 }{ 2 } \)bh.sq.feet
= \(\cfrac { 1 }{ 2 } \times 6\times 8\)
= 3 \(\times\) 8 = 24 feet
\(\therefore\) P = 24 feet, A = 24 sq. feet

Side of the Square (s) = 8 cm
P = 4s
P = 4 \(\times\) 8 = 32 cm
Area = S²
= 82 = 64 cm²

Length (l) = 6 m
breadth (b) = 4 m
Perimeter of the rectangle (P) = 2 (1+b) units
= 2 (6 + 4)
= 2(10) = 20m
Area(A) = l\(\times\)b = (6 \(\times\) 4)m²
= 24m
\(\therefore\) P = 20 m, A = 24 m²