Quick questions on Pythagoras theorem explained: O-Level E-Maths

Pythagoras extends to solids by applying it twice. To find the space diagonal of a cuboid with edges $a$, $b$ and $c$, first find the diagonal of the base, $\sqrt{a^2 + b^2}$, then use that as one leg of a second right triangle whose other leg is the height $c$. This gives the space diagonal $\sqrt{a^2 + b^2 + c^2}$. So a box measuring $3 \times 4 \times 12$ has a space diagonal of $\sqrt{9 + 16 + 144} = \sqrt{169} = 13$.

A Pythagorean triple is a set of three whole numbers satisfying $a^2 + b^2 = c^2$, such as $(3, 4, 5)$, $(5, 12, 13)$ and $(8, 15, 17)$. Spotting one, or a multiple of one like $(6, 8, 10)$, lets you write down the missing side without a calculator. If a right triangle has legs $9$ and $12$, recognising these as $3 \times (3, 4)$ gives the hypotenuse $3 \times 5 = 15$ instantly. Memorising the common triples and their multiples is a quick-win that saves time and provides a check on a calculated answer.

A right-angled triangle has legs $9\ \text{cm}$ and $40\ \text{cm}$. Find the hypotenuse. [2 marks]

The hypotenuse is $25\ \text{cm}$ and one leg is $7\ \text{cm}$. Find the other leg. [2 marks]

Is a triangle with sides $6\ \text{cm}$, $8\ \text{cm}$ and $11\ \text{cm}$ right-angled? [2 marks]