Question

the area of a rectangle is given by 6x²+19x+15. if x represents 4m, what are the dimensions of the length and width of the rectangle?​

Answer 1

Length = 17m

Width = 11m

Explanation:

Expression for the area of the rectangle = 6x² + 19x + 15

Factorising the quadratic expression

6x² + 19x + 15 = (6x² + 9x) + (10x + 15) = 3x(2x + 3) +5(2x + 3) = (3x + 5)(2x + 3)

x = 4m

Length = 3x + 5 = 3(4) + 5 = 12 + 5 = 17m

Width = 2x + 3 = 2(4) + 3 = 8 + 3 = 11m