Yes. If the ramp is 24 in. high and 72 in. long, the slope will be 2472= 0. 3, which is less than the maximum slope of 411= 0. 36.
Practice makes perfect
Let's answer the questions from the exercise to decide if we can use the given funbox plan to build the ramp to meet the safety regulations.
What Information Do You Have?
We are given a funbox plan with the total length and height of the ramp. Notice that we can use this information to find its slope.
Review that we can find the slope by calculating the ratio of the vertical change — the rise — to the horizontal change — the run.
m= rise/run
We can tell that in this case the rise is 24 and run is 72. Let's substitute these values in this formula and simplify to find the slope of the ramp!
m_(ramp)= 24/72 =1/3
How can you compare slopes?
Finally, we want to compare the slope of the ramp 13 to the maximum slope 411. To do it, we need to rewrite them with a common denominator. In this case it will be 33, as this is the least common denominator. Let's expand 13 by 11 and 411 by 3.
Fraction
Expand
Simplify
1/3
1 * 11/3 * 11
11/33
4/11
4 * 3/11 * 3
12/33
Now that we have the slopes with a common denominator, we can compare them!
11/33 <12/33 ⇔ 1/3 < 4/11
We can conclude that the maximum slope is greater than the slope of the ramp. Therefore, we can use the given funbox to build the ramp and meet the safety regulations.
