The diagonal of a rectangle is 17c.m. long and the perimeter of the rectangle is 46 c.m. Find the area of the rectangle.
Please tell me how to solve this problem.
Lets say , a is length and b is breadth of rectangle
Perimeter = 2(a+b) = 46
a+b = 23
b = 23 - a
Diagonal =
a^2 + a^2 + 529 - 46a = 289
2a^2 - 46a + 240 = 0
a^2 - 23a + 120 = 0
The value that we will get as a can be either length or breadth (as even if you solved for b you would have recieved same equaion)
Hence area = Lengt*Breadth = Multiplication of roots of this quadratic equation
-----------------------
For an equation
lx^2 +mx +n = 0
Multiplication of roots = n/l
-----------------
So here it will be = 120