Question
A slide is 8.9 feet long and 4.6 feet 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.
feet
feet
Answers
GPT-4o mini
To find the length of the base of the slide, we can use the Pythagorean theorem. The slide forms a right triangle where the length of the slide is the hypotenuse, the height is one leg of the triangle, and the base is the other leg.
Let:
- \( a \) = height of the slide = 4.6 feet
- \( c \) = length of the slide = 8.9 feet
- \( b \) = length of the base (which we want to find)
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Substituting the known values:
\[ (4.6)^2 + b^2 = (8.9)^2 \]
\[ 21.16 + b^2 = 79.21 \]
Now, subtract \( 21.16 \) from both sides:
\[ b^2 = 79.21 - 21.16 \]
\[ b^2 = 58.05 \]
Next, take the square root of both sides to solve for \( b \):
\[ b = \sqrt{58.05} \]
\[ b \approx 7.6 \]
Thus, the length of the base, rounded to the nearest tenth, is approximately \( 7.6 \) feet.
Let:
- \( a \) = height of the slide = 4.6 feet
- \( c \) = length of the slide = 8.9 feet
- \( b \) = length of the base (which we want to find)
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Substituting the known values:
\[ (4.6)^2 + b^2 = (8.9)^2 \]
\[ 21.16 + b^2 = 79.21 \]
Now, subtract \( 21.16 \) from both sides:
\[ b^2 = 79.21 - 21.16 \]
\[ b^2 = 58.05 \]
Next, take the square root of both sides to solve for \( b \):
\[ b = \sqrt{58.05} \]
\[ b \approx 7.6 \]
Thus, the length of the base, rounded to the nearest tenth, is approximately \( 7.6 \) feet.