Perimeter of a square and a rectangle are equal. If the perimeter of the square is 40 cm and the length of the rectangle is 2 cm more than the side of the square. Find the area of the rectangle.
Answers
Answer:
Step-by-step explanation:
Given : Perimeter of a square = Perimeter of a rectangle
Perimeter of a square = 4 X sides = 4a cm.
where a= side of the square
Perimeter of a rectangle = 2(l+b) cm
where l = length and b = breadth of the rectangle
Therefore 4a = 2( l+ b) = 40 cm.
Length of the rectangle is 2 cm more than the side of the square.
Hence l = a + 2. Substituting in the formula for perimeter,
2[ (a+2) + b ] = 40
2a + 4 + 2b =40
2a+ 2b = 40- 4
2 (a + b) = 36
Therefore (a+b) = 36 /2 = 18 cm.
Since 4a = 40 cm , a = 40/4 =10 cm.
Therefore length of the rectangle = a+2 = 10+2 = 12 cm.
To find the breadth, use the perimeter formula for a rectangle.
2( l+ b) = 40 cm
2( 12 +b)= 40 cm
24 + 2b = 40
Hence 2b = 40-24 = 16cm
b = 16/2 = 8 cm
Area of a rectange = length X breadth sq.cm
= 12 X 8
= 96 sq.cm.