A ladder is against a wall such that the base is 6 ft away from the wall. If the distance up the wall is 3 ft shorter than the length of the ladder, how long is the ladder?
the ladder is2 cm
a = 6 Ft.
b = c-3.
c = ?
a^2 + b^2 = c^2.
6^2 + (c-3)^2 = c^2.
36 + c^2-6c+9 = c^2.
36 - 6c = -9.
-6c = -45.
c = 7.5 Ft. = Length of ladder.
Correction: Math-99Henry. should be Math
Henry.
To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's denote the length of the ladder as "x" and the distance up the wall as "x - 3". The base of the ladder is given as 6 ft.
According to the Pythagorean theorem, we have:
x^2 = (x - 3)^2 + 6^2
Expanding the equation:
x^2 = x^2 - 6x + 9 + 36
Combining like terms:
0 = -6x + 45
Rearranging the equation:
6x = 45
Dividing both sides by 6:
x = 7.5
Therefore, the length of the ladder is 7.5 ft.