I need to find the value of p in a right triangular prism when the surface area is 457.25.

"P" is the distance between the bases
The triangleular base is 9.9 x 6.2
choices are:
16.65
8.75
14.25
9.45

Thank you-could you explain how you got the answer

To find the value of p, we need to know the formula for the surface area of a right triangular prism. The surface area of a right triangular prism is given by the formula:

SA = 2(Ab) + Ph

Where SA is the surface area, Ab is the area of the triangular base, P is the perimeter of the triangular base, and h is the height of the prism.

First, we need to calculate the area of the triangular base. The formula for the area of a triangle is:

Ab = 0.5 × base × height

Given that the base of the triangular base is 9.9 and the height is 6.2, we can calculate the area of the triangular base:

Ab = 0.5 × 9.9 × 6.2 = 30.87

Next, we need to find the perimeter of the triangular base. The perimeter is the sum of all sides. In this case, since we only have the base dimensions, we can calculate it by adding all sides of the triangle:

P = 9.9 + 9.9 + 6.2 = 26

Now, we have the values for Ab and P, so we can substitute them into the surface area formula:

457.25 = 2(30.87) + 26h

Now, we need to isolate h to solve for it. Start by simplifying:

457.25 = 61.74 + 26h

Subtract 61.74 from both sides:

457.25 - 61.74 = 26h

395.51 = 26h

Finally, divide both sides by 26 to solve for h:

h = 395.51 / 26 = 15.21

Therefore, the height of the prism is 15.21.

Since p is the distance between the bases, it is equal to the height:

p = 15.21

Therefore, the value of p in the right triangular prism with a surface area of 457.25 is approximately 15.21.

None of the provided choices match this value.

To find the value of "p" in the right triangular prism, we need to use the formula for the surface area (SA) of a right triangular prism.

The formula for the surface area of a right triangular prism is:
SA = 2LW + LH + WH

In this case, we know that the surface area is 457.25. Therefore, we can set up the equation:

457.25 = 2(9.9)(6.2) + (9.9)(p) + (6.2)(p)

Now let's solve for "p". First, let's simplify the equation:

457.25 = 122.76 + 9.9p + 6.2p

Combine the like terms on the right side of the equation:
457.25 = 122.76 + 16.1p

Subtract 122.76 from both sides of the equation:
334.49 = 16.1p

Now, divide both sides of the equation by 16.1 to isolate "p":
p = 334.49 / 16.1

Calculating p on your own:

p ≈ 20.74

Therefore, the value of "p" is approximately 20.74.

However, none of the provided choices match this value. Therefore, it seems that there may be an error in the question or the options.