Answer:
Length of AC = 12units.
Step-by-step explanation:
[tex]\sf\large{\star Given:-}[/tex]
- Hypotenuse of the triangle = [tex]\sf\pink{10\:units.}[/tex]
- Height of the triangle = [tex]\sf\pink{8 \: units.}[/tex]
[tex]\sf\large{\star To\: Find:-}[/tex]
[tex]\rightarrow[/tex] Base of the triangle.
[tex]\sf\large{\star Solution:-}[/tex]
[tex]\rightarrow[/tex]As we know that,
Pythagoras Theorem:
[tex]\sf\blue{Hypotenuse^2\:=\: Height^2+Base^2}[/tex]
So, In triangle ABD by putting the value of hypotenuse and height in this formula we get,
[tex]\rightarrow[/tex][tex]\sf{10^2\:=\: 8^2 + Base^2}[/tex]
[tex]\rightarrow[/tex][tex]\sf{100\:=\: 64 + Base^2}[/tex]
[tex]\rightarrow[/tex][tex]\sf{100-64\:=\: Base^2}[/tex]
[tex]\rightarrow[/tex][tex]\sf{36\:=\: Base^2}[/tex]
[tex]\rightarrow[/tex][tex]\sf{\sqrt{36}\:=\: Base}[/tex]
[tex]\rightarrow[/tex][tex]\sf{6\:=\: Base}[/tex]
Since, it is given that BD is the perpendicular bisector of AC so length of AC will be doubled.
Therefore, length of AC of the given triangle = [tex]\sf\purple{12units.}[/tex]
