Answer
(a) GD = $5\sqrt 2$
(b) GB = $5\sqrt 3$
Work Step by Step
(a)
Each face of a cube is a square and a diagonal divides it into two 45°–45°–90° triangles. Therefore-
In 45°–45°–90° triangle GCD
Diagonal GD = $\sqrt 2 \times $ CD
GD = $\sqrt 2 \times $ 5 ( CD is the edge of cube given as 5)
GD = $5\sqrt 2$
(b) GDB is a right triangle, right angled at D. Applying Pythagorean theorem-
$GB^{2} $ = $GD^{2} $ + $DB^{2} $
$GB^{2} $ = $(5\sqrt 2)^{2} $ + $5^{2} $ [DB is the side of cube given equal to 5]
$GB^{2} $ = $50 + 25 $ = 75
Therefore-
GB = $\sqrt 75$ = $\sqrt (25\times3)$
GB = $\sqrt 25 \times \sqrt 3$
GB = $5\sqrt 3$
