A ladder leans against a vertical wall of height 5m.if the foot of the ladder is 12m away from the wall, calculate the length of the ladder
Given that the ladder leans against a vertical wall of height 5m and the foot of the ladder is 12m away from the wall, we can use the Pythagorean theorem to find the length of the ladder.
According to the Pythagorean theorem, the square of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides. Let's assume the length of the ladder is "L".
So, by applying Pythagorean theorem, we have:
L^2 = Length of the vertical side^2 + Length of the horizontal side^2
L^2 = (5m)^2 + (12m)^2
= 25m^2 + 144m^2
= 169m^2
Taking the square root of both sides, we get:
L = √(169m^2)
= √(13^2 * m^2)
= 13m
Therefore, the length of the ladder is 13m.
To find the length of the ladder, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
In this case, the wall, the ground, and the ladder form a right-angled triangle.
Let's call the length of the ladder "l". The height of the wall is 5m, and the distance between the foot of the ladder and the wall is 12m.
According to the Pythagorean theorem:
l^2 = 5^2 + 12^2
l^2 = 25 + 144
l^2 = 169
To find the length of the ladder, we take the square root of both sides:
√l^2 = √169
l = 13
Therefore, the length of the ladder is 13 meters.