Question

What is the length of AC?

Answer 1

Answer:

Length of AC = 12units.

Step-by-step explanation:

$\sf\large{\star Given:-}$

• Hypotenuse of the triangle = $\sf\pink{10\:units.}$
• Height of the triangle = $\sf\pink{8 \: units.}$

$\sf\large{\star To\: Find:-}$

$\rightarrow$ Base of the triangle.

$\sf\large{\star Solution:-}$

$\rightarrow$As we know that,

Pythagoras Theorem:

$\sf\blue{Hypotenuse^2\:=\: Height^2+Base^2}$

So, In triangle ABD by putting the value of hypotenuse and height in this formula we get,

$\rightarrow$$\sf{10^2\:=\: 8^2 + Base^2}$

$\rightarrow$$\sf{100\:=\: 64 + Base^2}$

$\rightarrow$$\sf{100-64\:=\: Base^2}$

$\rightarrow$$\sf{36\:=\: Base^2}$

$\rightarrow$$\sf{\sqrt{36}\:=\: Base}$

$\rightarrow$$\sf{6\:=\: Base}$

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 = $\sf\purple{12units.}$