a ladder is 100 m long and distance between bottom of the ladder and wall is 60m.what is the maximum size of the cube that can be placed between the wall and the ladder.; a ladder is 100 m long and distance between bottom of the ladder and wall is 60m.what is the maximum size of the cube that can be placed between the wall and the ladder.
Answers
Answer:
Edge of cube = 34.2857 m
Volume of cube = 40303 .2 m³
Step-by-step explanation:
Ladder is 100 m long
Distance between bottom of Ladder & wall = 60 m
Height of wall where ladder is reaching = H
H² = 100² - 60²
=> H² = 10000 - 3600
=> H² = 6400
=> H = 80 m
Now to find maximum size of cube
let Say Cube has side = x m
if it is placed
there then we can see current triangle is divided into two right angle triangle & square
Area of current Triangle = (1/2) * Base * Height = (1/2) * 60 * 80 = 2400 m²
Area of bottom triangle = (1/2) * (60-x) * x
Area of Square = x²
Area of upper Triangle = (1/2) * x * (80-x)
Sum of all these = 2400 m²
(1/2) * (60-x) * x + x² + (1/2) * x * (80-x) = 2400
multiplying with 2 both sides
=> 60x - x² + 2x² + 80x - x² = 4800
=> 140 x = 4800
=> x = 480/14
=> x = 240/7
=> x = 34.2857 m
Volume of cube = (240/7)³ = 40303 .2 m³