Question

What is the measurement of the longest line segment in a right rectangular prism that is 16 centimeters long, 9 centimeters wide, and 7 centimeters tall? Round to the nearest tenth of a centimeter

Answer 1

We have been given that a rectangular prism is 16 centimeters long, 9 centimeters wide, and 7 centimeters tall. We are asked to find the measurement of the longest line segment in the prism.

We know that the longest segment will be the diagonal that will connect the two opposite corners at the top and bottom.

We know that diagonal of right triangular prism can be found using formula:

`d=√(w^2+l^2+h^2)`, where,

d = Diagonal,

w = Width

l = Length,

H = Height

Upon substituting our given values in diagonal formula, we will get:

`d=√(9^2+(16)^2+7^2)`

`d=√(81+256+49)`

`d=√(386)`

`d=19.6468827`

Upon rounding to nearest tenth of a centimeter, we will get:

`d\approx 19.6`

Therefore, the measure of the longest line segment would be 19.6 centimeters.