4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?

Correct result:

q1 =  1.362 m
q2 =  3.761 m

#### Solution:

$l=4 \ \\ f(x)=kx+q \ \\ f(1)=1 \ \\ f(x_{0})=0 \ \\ k=1/(1-x_{0}) \ \\ q=1-k \ \\ x_{01}=3.7609 \ \\ x_{02}=1.3622 \ \\ k_{1}=1/(1-x_{01})=1/(1-3.7609) \doteq -0.3622 \ \\ q_{1}=1-k_{1}=1-(-0.3622) \doteq 1.3622 \doteq 1.362 \ \text{m} \ \\ l_{1}=\sqrt{ q_{1}^2+x_{01}^2 }=\sqrt{ 1.3622^2+3.7609^2 } \doteq 4$
$k_{2}=1/(1-x_{02})=1/(1-1.3622) \doteq -2.7609 \ \\ q_{2}=1-k_{2}=1-(-2.7609) \doteq 3.7609 \doteq 3.761 \ \text{m} \ \\ l_{2}=\sqrt{ q_{2}^2+x_{02}^2 }=\sqrt{ 3.7609^2+1.3622^2 }=4$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Paper box
Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box?
• Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The
• Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.
• Minimum surface
Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
• Curve and line
The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
• Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
• Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
• Shopping malls
The chain of department stores plans to invest up to 24,000 euros in television advertising. All commercials will be placed on a television station where the broadcast of a 30-second spot costs EUR 1,000 and is watched by 14,000 potential customers, durin
• Summands
We want to split the number 110 into three summands so that the first and the second summand are in the ratio 4: 5, and the third with the first are in ratio 7: 3. Calculate the smallest of the summands.
• TV competition
In the competition, 10 contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors answered incorrectly in that round. One of the contestants after the contest said: We g
• The percent 2
The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5% respectively. Suppose you have 3200 to invest and you want to put twice as much in the growth fund as in the money market to maximize your return. How should you i
• Test scores
Jo's test scores on the first four 100 point exams are as follows: 96,90,76, and 88. If all exams are worth the same percent, what is the minimum test score necessary on his last exam to earn an A grade in the class (90% or better)?
• Minimum of sum
Find a positive number that the sum of the number and its inverted value was minimal.
• Classmates
Roman is ranked 12th highest and eleventh lowest pupil. How many classmates does Roman have?
• Ten boys
Ten boys chose to go to the supermarket. Six boys bought gum and nine boys bought a lollipop. How many boys bought gum and a lollipop?
• Hens and pigs
Hens and pigs have 46 feet in total. At least how much can heads have?
• Skoda cars
There were 16 passenger cars in the parking. It was the 10 blue and 10 Skoda cars. How many are blue Skoda cars in the parking?