a piece of a wire is bent to form a rectangle of are 72cm². if its length is twice its breadth. find the length of the wire
Answers
Step-by-step explanation:
Answer
Let the length and breadth of rectangle be 7x and 5x respectively.
perimeter of rectangle=length of wire
∴2(7x+5x)=72⇒24x=72⇒x=3
∴ Length of rectangle= 7×3=21cm
Breadth of rectangle =5×3=15
Area of rectangle =21×15=315cm
2
Answer :
The required length of the wire = 36 cm
Step-by-step explanation :
Given :
A piece of wire is bent to form a rectangle of area 72 cm²
the length is twice its breadth
To find :
the length of the wire
Solution :
Let L cm be the length of the rectangle and B cm be the breadth of the rectangle.
L = 2B
Area of the rectangle = length × breadth
72 cm² = L × B
72 = 2B × B
2B² = 72
B² = 72/2
B² = 36
B = √36
B = 6 cm
The breadth of the rectangle = 6 cm
The length of the rectangle = 2(6) = 12 cm
we have to find the length of the wire. Let it be "l cm"
Since the wire is bent to form a rectangle, the length of the wire is equal to the perimeter of the rectangle.
So, finding the perimeter of the rectangle :
➙ Perimeter of the rectangle = 2(Length + breadth)
➙ Perimeter of the rectangle = 2 ( L + B)
➙ Perimeter of the rectangle = 2 (12 + 6)
➙ Perimeter of the rectangle = 2 (18)
➙ Perimeter of the rectangle = 36 cm
The length of the wire is equal to the perimeter of the rectangle.
Therefore, the length of the wire = 36 cm