Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD =4, BD =6, what is the length of DC

Answer 1

Answer:

$AC=5$

Step-by-step explanation:

From the question we are told that:

Dimensions

$AD=4\\BD=6$

Generally the equation for these similar right triangle is mathematically given by

$\frac{AC}{AB}=\frac{AB}{AD}=\frac{BC}{BD}$

$\frac{AC}{AB}=\frac{AB}{AD}$

Where

$AD=x$

$AC=x+4$

Therefore

$AB^2=x(x+4)$

Generally the Pythagoras equation for $\triangle$ADB is mathematically given by

$AB^2=BD^2+AD^2$

$x(x+4)=4+x^2$

$x(x+4)-(4+x^2)=0$

$x^2+4x)-(4+x^2)=0$

$4x-4=0$

$x=1$

Therefore

$AC=x+4$

$AC=1+4$

$AC=5$