Given -
↠ the length of a rectangle is 11 m less than three times the width (let the width be x then length = 3x - 11)
↠the area of the rectangle is 42 m².
To find -
the dimensions of the rectangle.
Solution -
As we know,
area of rectangle = length × width
➟ 42 = (3x - 11) x
➟ 42 = 3x² - 11x
➟ 3x² - 11x - 42 = 0
now splitting the middle term to find the value of x,
➟ 3x² - (18 - 7)x - 42 = 0
➟ 3x² - 18x +7x - 42 = 0
➟ 3x (x- 6) +7(x - 6) = 0
➟ (3x + 7)(x - 6) = 0
➟ x = -7/3, 6
➟ x = 6
We will take the value of x as 6 because the value of dimensions can never be in negative.
Hence, length = 3 × 6 - 11 = 7 cm and width = 6 cm
