Answer :
Benton needs a 15-foot ladder to reach a height of 12 feet on the wall, so the answer is C.
To solve this problem, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms the hypotenuse, and the distance from the base of the ladder to the wall forms one of the other sides. Let's denote:
[tex]- \( a \)[/tex] as the distance from the base of the ladder to the wall (9 feet),
[tex]- \( b \)[/tex] as the height on the wall Benton needs to reach (12 feet), and
[tex]- \( c \)[/tex] as the length of the ladder.
We want to find the appropriate ladder length [tex]\( c \).[/tex]
According to the Pythagorean theorem:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
Plugging in the values we have:
[tex]\[ c^2 = 9^2 + 12^2 \][/tex]
[tex]\[ c^2 = 81 + 144 \][/tex]
[tex]\[ c^2 = 225 \][/tex]
Taking the square root of both sides to solve for [tex]\( c \):[/tex]
[tex]\[ c = \sqrt{225} \][/tex]
[tex]\[ c = 15 \][/tex]
So, Benton would need to use a 15-foot ladder to reach a height of 12 feet on the wall. Therefore, the answer is:
C. 15 feet
COMPLETE question:
Benton has an extension ladder than can only be used at a length of 10 feet, 15feet. or 20 feet. He places the base of the ladder 9 feet from the wall and needs the top of the ladder to reach 12 feet
Which lidder length would Benton need to use to reach this height on the wall?
A. 10 feet
B. None of these ladder lengths would reacti this height:
C. 15 feet
D. 20 feet
10 feet.
Think of it like this:
The wall is upright, it's 90° and it's 8 feet high. The distance from the bottom of the ladder to the bottom of the wall (along the ground, which is perpendicular to the wall) is 6 feet. When Benton places the base of the ladder 6 feet away from the wall and the top is resting at the top of the wall, it looks like a triangle, right?
Using pythagoras (this rule about right-angled triangles and stuff), we can already see that the two sides when simplified are 3:4. Because the 'triangle' is a right-angled triangle, the other side HAS to be 5 to complete the ratio. We just multiply it by 2 to get the correct ratio and that's your answer!
Think of it like this:
The wall is upright, it's 90° and it's 8 feet high. The distance from the bottom of the ladder to the bottom of the wall (along the ground, which is perpendicular to the wall) is 6 feet. When Benton places the base of the ladder 6 feet away from the wall and the top is resting at the top of the wall, it looks like a triangle, right?
Using pythagoras (this rule about right-angled triangles and stuff), we can already see that the two sides when simplified are 3:4. Because the 'triangle' is a right-angled triangle, the other side HAS to be 5 to complete the ratio. We just multiply it by 2 to get the correct ratio and that's your answer!
