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
The solution below is based upon the one
submitted by Anna of Parkside school. I liked the explanation of
how Anna arrrived at the factorisation.
The youngest person to send in a solution was
Sairah of Kings Park School, Lurgan and Barinder sent an excellent
solution with lots of clear explanation.
Just three of the large number of solutions to
this problem. Well done to you all!
I'll leave you to decide what 'square'
that is, but you might think of
something inspired just from looking at the algebra, or maybe
calculate the first line from the problem (it should come to $49$)
and take it from there .