A ladder 100 feet long is leaning against a vertical wall Its lower end is 60 foot from the bottom of the wall The side of the largest cubical box that can be placed between the wall and the ladder without disturbing the ladder is (to the nearest foot).
a) 26 b) 34 c) 21 d) 40; A ladder 100 feet long is leaning against a vertical wall Its lower end is 60 foot from the bottom of the wall The side of the largest cubical box that can be placed between the wall and the ladder without disturbing the ladder is (to the nearest foot).; a) 26 b) 34 c) 21 d) 40
Answers
Answer:
Option b
Step-by-step explanation:
Ladder is 100 feet long
Distance between bottom of Ladder & wall = 60 feet
Height of wall where ladder is reaching = H
H² = 100² - 60²
=> H² = 10000 - 3600
=> H² = 6400
=> H = 80 feet
Now to find maximum size of cube
let Say Cube has side = x feet
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 ft²
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 ft²
(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 = 34.28 ft
=> x = 34 ft
Option b is the right answer