A slide is 3 meters long and 2.3 meters high. How long is its base, from the bottom of the ladder to the end of the slide? If necessary, round to the nearest tenth.
meters
What is the length of the base of the slide?
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To find the length of the base of the slide, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case:
– The length of the slide (hypotenuse) is 3 meters.
– The height of the slide (one side) is 2.3 meters.
– We need to find the length of the base (the other side).
Using the Pythagorean theorem:
( a^2 + b^2 = c^2 )
Here, let:
– ( a = base )
– ( b = height = 2.3 ) meters
– ( c = length of the slide = 3 ) meters
Rearranging the formula to find the base:
( base^2 = slide^2 – height^2 )
Substituting in the values:
( base^2 = 3^2 – 2.3^2 )
Calculating:
( base^2 = 9 – 5.29 )
( base^2 = 3.71 )
Now, take the square root:
( base = sqrt{3.71} approx 1.9 )
So, the length of the base is approximately 1.9 meters when rounded to the nearest tenth.