A wire of length 140 cm is bent into a rectangle. If the length of the rectangle is 10 cm more than its breadth, find the area of the rectangle.
Answers
Answer:
The required area of the rectangle is 1200 cm²
Step-by-step explanation:
Given :
- A wire of length 140 cm is bent into a rectangle.
- The length of the rectangle is 10 cm more than its breadth.
To find :
the area of the rectangle
Solution :
As the wire is bent into a shape of rectangle, the length of the wire is equal to the perimeter of the rectangle.
we know,
Perimeter of the rectangle = 2(length + breadth)
Let 'l cm' be the length of the rectangle and 'b cm' be the breadth of the rectangle.
As given,
l = (b + 10) cm
Length of the wire = perimeter of the rectangle
140 cm = 2(l + b)
140 = 2(b + 10 + b)
140 = 2(2b + 10)
140/2 = 2b + 10
70 = 2b + 10
2b = 70 – 10
2b = 60
b = 60/2
b = 30 cm
The breadth of the rectangle is 30 cm.
Now, let's find the length of the rectangle.
length = 10 + 30 = 40 cm
Area of the rectangle = length × breadth
= 40 cm × 30 cm
= 1200 cm²
Answer:
1200 sq.cm
Step-by-step explanation: