The length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.
Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.
A builder makes all the ramps with a base to height ratio of 12 to 1 to be wheelchair accessible. Let k is the factor of ratio. Thus, the height and base is,
[tex]h=k\\b=12k[/tex]
The digram number 1 is similar to the right angle triangle in which the unknown side (say l) is hypotenuse. Thus, by the Pythagoras theorem,
[tex]l^2=(12k)^2+(k)^2\\l=\sqrt{144k^2+k^2}\\l=\sqrt{145k^2}\\l=\sqrt{145}k[/tex]
In the diagram below, which is not drawn to scale, a ramp needs to cover a height of 0.8 m. Height is equal to the factor k. Thus, the value of k is,
[tex]k=h\\k=0.8[/tex]
Thus, the length of the l is,
[tex]l=\sqrt{145}k\\l=\sqrt{13}\times0.8\\l=9.63\rm\; m[/tex]
Hence, the length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.
Learn more about the Pythagoras theorem here;
https://brainly.com/question/343682
