Question

A pyramid has rectangular base of length (3x+1) and a width x

it also has a perpendicular height of 12cm
the volume is 96cm^2
find the value of x?

Answer 1

(1/3)x(3x + 1)(12) = 96

4x(3x + 1) = 96

3x² + x = 24

3x² + x - 24 = 0

x = (-1 ± √(1² - 4(3)(-24)))/(2(3))

= (-1 ± √(1 + 288))/6

= (-1 ± √289)/6

= (-1 ± 17)/6

= 16/6 = 8/3 = 2 2/3

(-18/6 = -3 is extraneous)