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

`AC=5`

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

`(AC)/(AB)=(AB)/(AD)=(BC)/(BD)`

`(AC)/(AB)=(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`