FINDING LENGTH & BREADTH OF RECTANGLE OR SQUARE IF PERIMETER & SQUARE IS GIVEN -
Ø If the perimeter of a square is given, then side = Perimeter/ 4
Ø If the area of a square is given, then side = √area
Ø If the perimeter of a rectangle is given and length is given, then breadth = (P/2) - l
Ø If the perimeter of a rectangle is given and breadth is given, then length= (P/2) - b
Ø If the area of a rectangle is given and the length is given, then breadth = A/length
Ø If the area of a rectangle is given and the breadth is given, then length = A/breadth
Example.1) A wire is in a shape of a square of side 10cm. If the wire is rebent into a rectangle of length 12cm, find its breadth. Which shape encloses more area and by how much?
Ans.) As per the given condition,
Length of wire = perimeter of square = 4 X side
= 4 X 10cm = 40cm
Let the breadth of the rectangle be b cm.
We know, perimeter of a rectangle is = 2 (length + breadth)
As per the condition, 40cm = 2 (length + breadth)
Or, 20cm = (12cm + b) [replacement of l = 12cm]
Or, b = (20cm - 12cm) = 8cm
So, the breadth of the rectangle is 8cm.
Now we have to compare area of square & rectangle.
Area of square = 10cm X 10cm = 100cm²
Area of the rectangle is = 12cm X 8cm = 96cm²
So, the difference between square & rectangle is = 100cm²- 96cm²= 4cm²
Hence, square has more area by 4cm². (Ans.)
Example.2) The area of the square & rectangle are equal.If the side of the square is 40cm and the breadth of the rectangle is 25cm, find the length of the rectangle and also find the perimeter of the rectangle.
Ans.) As per the given condition,
area of the square is = 40cm X 40cm = 1600 cm²
Here, area of square = area rectangle
Let, length of the rectangle is 'l' and breadth is given 25cm.
So, l X 25 cm = 1600 cm²
1600 cm²
l = ------------ = 64 cm .............(i) (Ans.)
25 cm
So, the length of the rectangle is 64 cm.
Perimeter of the rectangle is = 2 (length + breadth)
= 2 (64 + 25)
= (2 x 89) = 178 cm ..........(ii) (Ans.)