Question

Find the value of b. Express the answer as a simplified radical.

Answer 1

Py Pythagoras theorem ,we can find value of b
(AC)^2=(AB)^2+(BC)^2
(14)^2=(b)^2+(8)^2
=>196=b^2+64
=>196-64=b^2
=>132=b^2
=>2root3 =b
Hope this helps u...!!

Answer 2

Here three sides of a right angled triangle given.

The three sides are b, 8 and 14.

The side with length 14 is the hypotenuse here. We have to find the side of length b.

To get b, we will use Pythagoras theorem here.

By using Pythagoras theorem we can write,

$c^2=a^2+b^2$, where c is the hypotenuse.

So here we can write,

$14^2=8^2+b^2$

$196 = 8^2+b^2$

$196=64+b^2$

To solve it for b, now we have to move 64 to the left side by subtracting it from both sides.

$196-64 = 64+b^2-64$

$196-64 = b^2$

$132=b^2$

Now to find b, we have to take square root to both sides. We will get,

$\sqrt{132}= \sqrt{b^2}$

$\sqrt{132} =b$

$b= \sqrt{(4)(33)}$

$b= (\sqrt{4})(\sqrt{33})$

$b= 2\sqrt{33}$

We have got the required answer for the side b.