Question

Packaging for a new type of cheese is being constructed in the shape of a right triangular prism. the cheesemaker wants the volume of the packaging to be 54 mm3. if the height of the cheese is 2 mm less than twice the base and length is 3 mm longer than twice the base, what must the base of the packaging be? (note: the volume of a right triangular prism is v = 1/2bhl.)

Answer 1

To find the base of the packaging, use the formula for the volume of a right triangular prism and solve an equation.

Step-by-step explanation:

To find the base of the packaging, we need to determine the values of the height and length using the given information. Let's assume the base of the packaging is 'b'.

According to the problem statement, the height is 2 mm less than twice the base, so the height is 2b - 2 mm. The length is 3 mm longer than twice the base, so the length is 2b + 3 mm.

To calculate the volume of the packaging, we use the formula for the volume of a right triangular prism:

V = (1/2) * b * h * l

Substituting the values we found for height and length into the formula:

V = (1/2) * b * (2b - 2) * (2b + 3)

We know that the volume should be 54 mm³. So we set up the equation:

54 = (1/2) * b * (2b - 2) * (2b + 3)

Solving this equation will give us the value of 'b', which is the base of the packaging.