Question
Ben is building a storage box for the sail of his boat. The left side of the box is 3 feet long and the right side of the box is 4 feet long. The left and right side form a right angle, as shown in the picture below.
Note: Figure is not drawn to scale.
What is the length of the base of the box?
A.
4.5 feet
B.
5 feet
C.
3.5 feet
D.
7 feet
Note: Figure is not drawn to scale.
What is the length of the base of the box?
A.
4.5 feet
B.
5 feet
C.
3.5 feet
D.
7 feet
Answers
GPT-4o mini
To find the length of the base of the box, we need to first recognize that the left side (3 feet) and the right side (4 feet) of the box form a right triangle. The left side can be considered one leg of the triangle and the right side the other leg.
We can use the Pythagorean theorem, which states that for a right triangle:
\[ a^2 + b^2 = c^2 \]
Here:
- \( a = 3 \) feet (one leg)
- \( b = 4 \) feet (other leg)
- \( c = \) hypotenuse (which we want to find)
Plugging in the values:
\[ 3^2 + 4^2 = c^2 \]
\[ 9 + 16 = c^2 \]
\[ 25 = c^2 \]
Now take the square root of both sides:
\[ c = \sqrt{25} \]
\[ c = 5 \text{ feet} \]
So, the length of the base of the box is 5 feet.
The answer is **B. 5 feet**.
We can use the Pythagorean theorem, which states that for a right triangle:
\[ a^2 + b^2 = c^2 \]
Here:
- \( a = 3 \) feet (one leg)
- \( b = 4 \) feet (other leg)
- \( c = \) hypotenuse (which we want to find)
Plugging in the values:
\[ 3^2 + 4^2 = c^2 \]
\[ 9 + 16 = c^2 \]
\[ 25 = c^2 \]
Now take the square root of both sides:
\[ c = \sqrt{25} \]
\[ c = 5 \text{ feet} \]
So, the length of the base of the box is 5 feet.
The answer is **B. 5 feet**.