2 extension ladders are leaning at the same angle against a vertical wall. The 3 meter ladder reaches 2.4 meters up the wall. How much farther up the wall does the 8 meter ladder reach?
To solve this problem, you can use the concept of similar triangles. Since both ladders are leaning at the same angle against the vertical wall, the ratios between their lengths and the heights they reach on the wall will be the same.
Let's assign variables to the given information:
Length of the first ladder (3 meter ladder) = 3m
Height reached by the first ladder = 2.4m
Length of the second ladder (8 meter ladder) = 8m
Height reached by the second ladder = x (unknown)
We can set up the following proportion:
(3m)/(2.4m) = (8m)/(x)
To find the value of x, we can cross-multiply and solve for x:
3m * x = 2.4m * 8m
3x = 19.2
Divide both sides by 3:
x = 19.2 / 3
x ≈ 6.4
Therefore, the 8-meter ladder reaches approximately 6.4 meters up the wall, which is 4 meters farther than the 3-meter ladder.
To solve this problem, we can use the concept of similar triangles.
Let's assume that the height reached by the 8 meter ladder is H meters.
We can set up a proportion based on the similar triangles formed by the ladders against the wall:
(Height reached by the 3 meter ladder) / (Length of the 3 meter ladder) = (Height reached by the 8 meter ladder) / (Length of the 8 meter ladder)
Substituting the given values, we have:
2.4 / 3 = H / 8
To solve for H, we can cross-multiply and then divide:
2.4 * 8 = 3 * H
19.2 = 3H
H = 19.2 / 3
H ≈ 6.4 meters
Therefore, the 8 meter ladder reaches approximately 6.4 meters up the wall, which is 4 meters further up than the 3 meter ladder.
3/8=2.4/L
solve for L.