Answer
h= $\sqrt[5] 3$
r=$\sqrt[5] 6$
y=5
x=10
Work Step by Step
Step 1:
$45^{\circ} - 45 ^{\circ} -90^{\circ}$ triangle , Now let s be the shorter side .
Let r be the longest side, which is the hypotenuse .
It has been shown in the section 1.1 that r= $\sqrt 2s$
Step 2:
Triangle ADC is $45^{\circ}-45^{\circ}-90^{\circ}$ triangle .
Using the above result,
r=$\sqrt[s] 2=\sqrt[5] 3(\sqrt 2)=\sqrt[5] 6$.
Since the legs are of equal length , h=r=$\sqrt[5] 3$
Step 3:
In $30^{\circ}-60^{\circ}-90^{\circ}$ triangle, let us consider y be the shortest side.
Let x be the longest side, which happens to a hypotenuse and h be the side opposite $60 ^{\circ}$ angle.
It is shown in section 1.1 that x=2y and h=$\sqrt 3y$
Step 4
Triangle CDB is $30^{\circ}-60^{\circ}-90^{\circ}$ triangle .
We are given that h=$\sqrt[5] 3$.
U?sing the above result,
y=$\frac{h}{\sqrt 3}=5$
and x=2y=10
