The surface area of a rectangular prism is 190 square inches, the length is 10 inches, and the width 3 inches. Find the height.
I know how to do SA but I don't understand how to find height if you have SA given. The answer is 5 in but I am not able to come up with the right answer.
To find the height of a rectangular prism when the surface area is given, you need to understand how the surface area formula relates to the dimensions of the prism.
The surface area of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh, where "l" represents length, "w" represents width, "h" represents height, and SA represents the surface area.
In this case, the surface area is given as 190 square inches, the length is 10 inches, and the width is 3 inches. We can substitute these values into the formula and solve for the height.
190 = 2(10)(3) + 2(10)h + 2(3)h
190 = 60 + 20h + 6h
190 = 60 + 26h
To isolate the "h" term, subtract 60 from both sides:
190 - 60 = 60 + 26h - 60
130 = 26h
Next, divide both sides of the equation by 26 to solve for "h":
h = 130 / 26
h = 5
Therefore, the height of the rectangular prism is 5 inches.
To summarize the steps:
1. Use the surface area formula: SA = 2lw + 2lh + 2wh.
2. Substitute the given values into the formula.
3. Simplify the equation and isolate the "h" term.
4. Solve for "h" by performing the necessary calculations.
5. The result will be the height of the rectangular prism.
To find the height of a rectangular prism given the surface area, you need to use the formula for the surface area of a rectangular prism. The formula is:
Surface Area = 2lw + 2lh + 2wh
In this case, the surface area is given as 190 square inches, the length is 10 inches, and the width is 3 inches.
Plugging in these values into the formula, we have:
190 = 2(10)(3) + 2(10)(h) + 2(3)(h)
Simplifying:
190 = 60 + 20h + 6h
Combine like terms:
190 = 60 + 26h
Subtract 60 from both sides:
190 - 60 = 26h
130 = 26h
Divide both sides by 26:
130/26 = h
Simplifying:
5 = h
So, the height of the rectangular prism is 5 inches.
let the missing dimension be x in
SA = 2(10)(3) + 2(10)(x) + 2(3)(x)
190 = .....
solve for x