:= Question Help
What is the longest line segment that can be drawn in a right
rectangular prism that is 12 cm long, 11 cm wide, and 10 cm tall?

Longest line segment: 12.89 cm

Step-by-step explanation:

Right Rectangular Prism

A right rectangular-based prism has a height measured from the center of the base up to the top of the prism. The longest line segment can be:

1. Any of the provided dimensions of the base or

2. A drawn line from the top ending in any of the corners of the base. It's the hypotenuse of a triangle whose legs are: the height of the prism and half the diagonal of the rectangle of the base.

The construction of the triangles can be seen in the figure attached. The line segment we are required to compute is the solid red line.

Let's first compute the diagonal of the rectangle of sides 12 cm and 11 cm.

Half of the diagonal is

Finally, we find the hypotenuse of the triangle formed by d/2, h, and the required distance, let's call it p

This length is greater than the 12 cm side of the rectangle, so it confirms our initial guess, the longest line segment is 12.89 cm long.

Note if the height would have been, for example, 5 cm, the longest line would have been 12 cm, and not the one found by the procedure

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.