Question

A trough at the end of a gutter spout is meant to direct water away from the house. The

homeowner makes the trough from a rectangular piece of of aluminum that is 20 in. long and 12
in. wide. He makes a fold along the long sides a distance of x inches from the edge. If he wants the
trough to hold 360 in³ of water, how far from the edge should he make the fold?

Answer 1

Answer:20 in * (12 in - 2X in) * (X in) = 360 in3

This can be simplified by dividing both sides by 20 in:

20 in * (12 in - 2X in) * (X in) = (360 in3/ 20 in)

After dividing both sides by 20 in:

(12 in - 2X in) * X in = 18 in2

Distribute X in. across (12 in -2X in):

12X in2 - 2X2 in2 = 18 in2

1.Subtract 18 in2 from both sides:

12X in2 - 2X2 in2 - 18 in2 = 0

2. Rearrange the equation:

-2X2 in2 + 12X in2 - 18 in2 = 0

This for matches the form for a quadratic equation (Ax2 + Bx +C = 0)

You can then plug these values into the quadratic formula to solve for X

so your answer is X=3