Can you make a tetrahedron whose faces all have the same perimeter?
A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
What is the area of the quadrilateral APOQ? Working on the building
blocks will give you some insights that may help you to work it
We had a number of correct answers to
this problem. Several solutions used a spreadsheet, for example the
one shown below is from an anonymous solver. We also received a
solution from someone who has done some calculus and was able to
solve the problem using this approach. I have included this
solution at the end for those of you who are interested.
My disappointment is that some of you are
still just sending in answers without explanation and I do want to
see how you arrived at your answers. Although the solution below
was found using a spreadsheet you might have used a calculator and
carried out a standard "trial and improvement" process to obtain
the same result.
Catherine, Ellean, Anna from The Mount School,
York add the following comment which means they were really
thinking about the numbers and the context...
Andisheh of Springfield School offered
the following explanation (well done):
Andisheh attached a spreadsheet and I
have used this and several other solutions employing a spreadhsheet
to create the extract below: Solvers were able to find that the
minimum time occurred with a distance between 76 and 77m and then
worked with one and then two decimal places to obtain greater
The final solution was sent in by an anonymous
solver who used calculus (a branch of mathematics normally met for
the first time at advanced level in the UK). It is a neat solution
but this high level mathematics was certainly not required!