Question

Find the missing length indicated. Leave your answer in simplest radical form.A) find the shortest leg of the hypotenuse (d)B) what is the entire hypotenuse (h)C) what is the longest leg (a)D) find the shortest leg (b)

Answer 1

Given:

The right triangle with bisector length 3120 and hypotenuse length 6400+x.

Required:

Find the x.

Step-by-step explanation:

We will redraw figure first

First we will apply Pythagoras theorem on triangle ADB

`\begin{gathered} Base^2+perpendicular^2=hypotenuse^2 \\ 3120^2+6400^2=AB^2 \\ AB=7120 \end{gathered}`

Now, we will apply on BDC

`3120^2+x^2=BC^2`

Now, in triangle ABC

`\begin{gathered} 7120^2+x^2+3120^2=(6400+x)^2 \\ 7120^2+x^2+3120^2=6400^2+x^2+2*6400* x \\ 7120^2+3120^2=6400^2+12800x \\ x=1521 \end{gathered}`

Answer:

The value of x is 1521.