Question

the length of a rectangle is 8 m less than thrice its width. if area of the rectangle is 1675 sq m them find the length and width of the rectangle

Answer 1

let the width is x m
therefore breadth = 3x-8
According to question
Area of rectangle = 1675 sq m
length × breadth = 1675 sq m
(3x-8)x = 1675
3x^2 - 8x = 1675
3x^2 - 8x - 1675 = 0
3x^2 - (75 - 67)x - 1675 = 0
3x^2 - 75x + 67x - 1675 = 0
3x(x - 25) + 67(x - 25) = 0
(x - 25)(3x + 67) = 0
therefore x = 25 and x = - (67/3)
since x is a side of rectangle and it can't be a negative value therefore,
x = 25 = width of rectangle.
length = 3x - 8 = 3(25) - 8 = 75 - 8 = 67
(25m, 67m) Ans