The area of a rectangle is 108m2 and its diagonal is 15m. Find the perimeter of the rectangle if the sides are of integer lengths.

Accepted Solution

Considering the figure, In ΔABC, right angled at B, we can use Pythagoras theorem :[tex] x^2 + y^2 = 15^2 [/tex][tex] x^2 + y^2 = 225 [/tex]..................(1)Also we are given area of rectangle as 108 m²Area of rectangle = length * breadth = x * y[tex]108 =x*y[/tex].............(2)[tex]x=108/y[/tex]........(3)plugging the value of x from equation (3) in (1),[tex] x^2 + y^2 = 225 [/tex][tex] (108/y)^2 + y^2 = 225 [/tex]We can use quadratic formula to solve this.On solving this we get four values of y as :y=12, y=-12, y=9 and y=-9since length cannot be negative we have two y values as :y=12 and y=9plugging these in equation (3) to get x as x=108/y = 108/12 = 9x = 108/9 =12so we have two answers:length =9 m and breadth = 12mlength =12 m and breadth =9mPerimeter = 2(l+b)Perimeter = 2(9+12) = 42m