Answer:
a) For [tex]x=7[/tex] units
[tex]y=7\sqrt2[/tex] units
b) For [tex]y=7\sqrt 6[/tex] units
[tex]x=7\sqrt 3[/tex] units
c) For [tex]x=\sqrt 3[/tex] units
[tex]y=\sqrt6[/tex] units
d) For [tex]y=4[/tex] units
[tex]x=\frac{4\sqrt 2}{2}[/tex] units
Step-by-step explanation:
Given triangle is a special 45-45-90 triangle.
Using the property of this triangle, if length of each leg is [tex]x[/tex] units then
[tex]Hypotenuse = x\sqrt2[/tex] units.
For the given table [tex]x[/tex] is length of each leg of the right triangle and [tex]y[/tex] represents the length of hypotenuse.
a) For [tex]x=7[/tex] units
[tex]y=7\sqrt2[/tex] units
b) For [tex]y=7\sqrt 6[/tex] units
[tex]x=\frac{7\sqrt 6}{\sqrt2}=\frac{7\sqrt {2}\sqrt3}{\sqrt2}=7\sqrt 3[/tex] units
c) For [tex]x=\sqrt 3[/tex] units
[tex]y=\sqrt 3\sqrt2=\sqrt6[/tex] units
d) For [tex]y=4[/tex] units
[tex]x=\frac{4}{\sqrt2}[/tex] units
On simplifying.
[tex]x=\frac{4\times \sqrt 2}{\sqrt2\times \sqrt2}[/tex]
[tex]x=\frac{4\sqrt 2}{2}[/tex] units
