IKMC 2024 - Grades 11-12 - Self-study Question 13

Question 13

Four squares are arranged as shown above a horizontal baseline. The smaller side lengths are a, b, c. Vertices A, C are opposite vertices of the large square, and B lies on one of its sides. Which expression equals its side length?

Question illustration

$\frac12(a+b+c)$
$\sqrt{a^2+b^2+c^2}$
$\sqrt{(a+b)^2+c^2}$
$\sqrt{(b-a)^2+c^2}$
$\sqrt{a^2+ab+b^2+c^2}$