Steve is building a slide for a new park. He wants the height of the slide to be 6 feet, and he wants the horizontal distance along the ground to measure 14 feet.
After building the slide, Steve decides the slide needs a vertical safety support and wants to use a 3-foot piece of wood to build the support. How far from the point where the base of the slide meets the ground should Steve place the vertical support?
After cross multiplying, I found the answer of 7 feet. Did I answer this correctly?
7.68
To determine the correct placement of the vertical support for Steve's slide, we need to use similar triangles.
Let's create a right triangle to represent the slide. The height of the slide (the vertical side) is 6 feet, and the horizontal distance along the ground (the base of the triangle) is 14 feet. The vertical support (another vertical side) is 3 feet.
By using the concept of similar triangles, we can set up a proportion:
(Height of slide)/(Horizontal distance along the ground) = (Height of vertical support)/(Distance from the base of the slide to the vertical support)
Plugging in the values we know:
6 feet / 14 feet = 3 feet / (Distance from the base of the slide to the vertical support)
Cross multiply this proportion:
6 feet * (Distance from the base of the slide to the vertical support) = 14 feet * 3 feet
Simplifying:
6 * (Distance from the base of the slide to the vertical support) = 42
Divide both sides by 6 to solve for (Distance from the base of the slide to the vertical support):
(Distance from the base of the slide to the vertical support) = 42 / 6 = 7 feet
Therefore, the vertical support should be placed 7 feet from the point where the base of the slide meets the ground.
So, yes, you have correctly answered the question. The vertical support should be placed 7 feet from the base of the slide.