Deductive Geometry

Question

a water slide is 4.2m high and has a support 2.4m tall. if a student reaches this support when she is 3.1m down the slide, how long is the slide ? i know the answer is 7.23 but have no idea what to do after i find the adj of the small triangle (2.5m) 

Answer 1

Yes, sir. Indeed the supporting beam forms two similar right triangles with heights 4.2 and 2.4 as given in the problem.

 

Let x represent the hypotneuse of the smaller triangle, which also symbolizes the rest of the slide.

As stated, she already went 3.1 meters down the slide when she is at the supporting beam.

She has X meters left to go.

 

Similar triangles have sides that are directly proportional.

 

So    X/2.4  = (x + 3.1)/4.2

 

 

Cross multiplication results in  4.2X = 2.4(x + 3.1)

 

                                            42X = 24(x + 3.1)  <--- multiplies both sides by 10 to clear the decimals

 

                                            42X = 24X + 74.4  <-- distributive right side

 

                                             42X - 24X = 74.4

 

                                            18X = 74.4

 

                                             X = 74.4/18 = 4.13333..... = 4.13 

 

So the length of the slide is 3.1+4.13 = 7.23

 

 

Just as a check, the ratio of the heights to the hypotneuses are:

 

   4.2/7.23   = 2.4 / 4.13 = 0.58064516129....