Question

The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm
The height of the open box is (x - 2) cm.
a) Show that 2x + 5x -58 = 0
) Solve the equation 2x + 5x -58 = 0, giving your answers correct
to 2 decimal places
D) Hence calculate the volume of the box, stating the units of your answer.

Answer 1

Answer:

a) x = 8.29 cm

D) V = 1125.27 cm³

Step-by-step explanation:

a) We can solve the equation as follows:

$2x + 5x - 58 = 0$

$2x + 5x = 58$

$x = \frac{58}{7} = 8.29$

D) The volume of the box is given by:

$V = l*w*h$

Where:

l: is the length

w: is the width

h: is the height

The length of the rectangular box is:

$l = (2x + 5) cm = (2*8.29 + 5) cm = 21.58 cm$

The width is x = 8.29 cm.

And the height is:

$h = (x - 2) cm = (8.29 - 2) cm = 6.29 cm$

Hence, the volume is:

$V = l*w*h = (21.58*8.29*6.29) cm^{3} = 1125.27 cm^{3}$

I hope it helps you!