Question

Perimeteris 180 . Find length and breadth

Answer 1

Given a perimeter of 180, the length and width of the rectangle with maximum area are 45 and 45.

Explanation:

Let x= the length and y= the width of the rectangle.
The area of the rectangle A=xy

2x+2y=180 because the perimeter is 180.

Solve for y
2y=180−2x
y=90−x

Substitute for y in the area equation.
A=x(90−x)
A=90x−x2

This equation represents a parabola that opens down. The maximum value of the area is at the vertex.

Rewriting the area equation in the form ax2+bx+c
A=−x2+90xaaaa=−1,b=90,c=0

The formula for the x coordinate of the vertex is
x=−b2a=−902⋅−1=45

The maximum area is found at x=45
and y=90−x=90−45=45

Given a perimeter of 180, the dimensions of the rectangle with maximum area are 45x45.

Answer 2

If the perimeter is 180 the length and breadth of the perimeter is 45

Verification:
Perimeter of rectangle= 2(l+b)
=2(45+45)
=2(90)
=180
Perimeter of square = 4*side
=4*45
=180
#Be Brainliest
#Be Logical