mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Square in a triangle

Source: Maths Jam
A right-angled triangle has short sides of length \(a\) and \(b\). A square is drawn in the triangle so that two sides lie on the sides of the triangle and a corner lies on the hypotenuse.
What is the length of a side of the square?

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths XXX,
puzzles about geometry, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

products probabilty gerrymandering functions lines lists rugby scales tournaments unit fractions doubling integration dates circles tangents even numbers star numbers cryptic crossnumbers dominos quadratics prime numbers square grids square roots complex numbers integers multiples area geometric mean factorials ellipses squares quadrilaterals logic neighbours dodecagons folding tube maps mean digital clocks albgebra 3d shapes axes triangles arrows number cubics digits averages consecutive numbers shapes shape xor expansions matrices hexagons time calculus decahedra prime factors pentagons crosswords fractions geometric means geometry menace planes surds crossnumbers money parabolas irreducible numbers 2d shapes christmas volume perfect numbers elections perimeter graphs symmetry floors means dice polygons odd numbers trigonometry triangle numbers differentiation determinants coins division books digital products proportion algebra speed sequences games pascal's triangle remainders spheres chess taxicab geometry multiplication regular shapes sum to infinity polynomials chocolate consecutive integers powers grids chalkdust crossnumber factors medians angles the only crossnumber partitions tiling balancing combinatorics indices wordplay routes bases cryptic clues range sums advent colouring multiplaction squares palindromes median binary percentages cube numbers ave square numbers coordinates clocks people maths sport cards addition sets probability numbers rectangles

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026