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.
Let x = height.
2(10*3) + 2(3x) + 2(10x) = 190
Solve for x.
To find the height of the rectangular prism, given the surface area, length, and width, you can use the formula for the surface area of a rectangular prism, which is given by:
SA = 2lw + 2lh + 2wh
In this case, you have the surface area (SA) as 190 square inches, the length (l) as 10 inches, and the width (w) as 3 inches. Let's denote the height as "h."
You can plug in these values into the formula and solve for h:
190 = 2(10)(3) + 2(10)(h) + 2(3)(h)
Expanding this equation gives:
190 = 60 + 20h + 6h
Combine like terms:
190 = 60 + 26h
Subtract 60 from both sides:
130 = 26h
Divide both sides by 26:
5 = h
Therefore, the height (h) of the rectangular prism is 5 inches.
To find the height of a rectangular prism when the surface area is given, you can use the formula for the surface area of a rectangular prism, which is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
In this problem, the surface area is given as 190 square inches, the length is 10 inches, and the width is 3 inches. Plugging the given values into the formula, we get:
190 = 2(10)(3) + 2(10)(h) + 2(3)(h)
Simplifying the equation, we have:
190 = 60 + 20h + 6h
Combining like terms:
190 = 60 + 26h
Subtracting 60 from both sides:
130 = 26h
Dividing both sides by 26:
5 = h
Therefore, the height of the rectangular prism is 5 inches.