Question

Garrett is building a slide for his kids. If the ladder is 1 meter tall and he wants the bottom of the slide to be 4 meters from the ladder, how long does the slide need to be?

Answer 1

The slide needs to be 4.123 meters

Step-by-step explanation:

Length for the ladder- 1 mtr

Distance of the bottom of the slide from the ladder- 4 mtr

Length of the slide needed

We can view the whole set up in the form of a right-angled triangle with the base representing the slide distance from the ladder, ladder length representing altitude and slide length representing as hypotenuse (As provided in the diagram)

For right-angled triangle we know from Pythagoras theorem-

Base² + altitude²= hypotenuse ²

Substituting the values of base as 4 mtr and altitude as 1 m

(Hypotenuse)²= 17

∴ Hypotenuse (slide length) =4.123 mtr

∴ Length of the slide needed= 4.123 meters

Answer 2

The length of the slide is 4.1231 meters. If the ladder is 1 meter tall and he wants the bottom of the slide of to be 4 meters from the ladder.

Step-by-step explanation:

         The given is,

                   the ladder is 1 meter tall

                   the bottom of the slide to be 4 meters from the ladder

Step:1

      Let, X = Length between bottom of ladder to slider

             Y = Tall of the ladder

             Z = Length of the slide

Step:2

       From given,

              X = 1 meter

              Y = 4 meters

Step:3

     Ref, the diagram. It is a right angle triangle,

     So, we apply Pythagoras's theorem

          $AC^{2}$ = $AB^{2}$ + $BC^{2}$

           $Z^{2}$ = $Y^{2}$ + $X^{2}$

Step:4

     Substitute the X and Y values,

           $Z^{2}$ = $4^{2}$ + $1^{2}$

           $Z^{2}$ = 16 + 1

           $Z^{2}$ = 17

          $Z$ = $\sqrt{17}$

          $Z$ = 4.123 meters

Result:

        Thus the length of the slide is 4.123 meter.