Question

perimeter of a rectangular plot is 180 m and its area is 1800 metre square the length of the plot as X metre use the perimeter 180 metre to write the value of breath in terms of x use the value of Length, breadth and area to write an equation in X solve the equation to calculate the length and breadth of the plot

Answer 1

Answer:

Step-by-step explanation:

Hi

let the length be x

and breadth be y.

Perimeter of rectangle = 2(l+b)

It is given that perimeter is 180 m.

So,  2(x+y) = 180

 x + y = 90

y = 90 - x  ..........(i)

Area of rectangle = lb

It is given that the area is 1800 m².

So, xy= 1800             .............(ii)

Putting value of y from (i) in (ii),

x(90-x) = 1800

90x - x² - 1800 = 0

Dividing whole equation by (-),

-90x +x² +1800 = 0

x² - 90x + 1800 = 0

x² - 60x - 30x + 1800 = 0

x (x-60) - 30(x-60) = 0

(x-30) (x-60)=0

x = 30  and x=60.

Hence, x = 30 m and 60 m.

Therefore, there are two possible lengths 30m and 60m.

and y = 90-x

= 90 - 30 = 60m 

and 90 - 60 = 30m.

Hence, two possible pair are length = 30m and breadth = 60m.

But, this is not possible as length is never greater to breadth.

So, the possible length is 60 m and breadth is 30 m.