Question

Find the value of $x$ . Write your answer in simplest form.

Answer 1

Consider the traingle as per the attachment

In
`{\triangle}`ADB. By Pythagoras theorem:

`{:\implies \quad \sf x^(2)+4^(2)=AB^(2)}`

`{:\implies \quad \sf AB^(2)=x^(2)+16\quad ...(i)}`

Now, In
`{\triangle}`ADC. By Pythagoras theorem:

`{:\implies \quad \sf x^(2)+9^(2)=AC^(2)}`

`{:\implies \quad \sf AC^(2)=x^(2)+81\quad ...(ii)}`

Now, In
`{\triangle}`BAC. By Pythagoras theorem:

`{:\implies \quad \sf AB^(2)+AC^(2)=BC^(2)}`

By (i) and (ii)

`{:\implies \quad \sf x^(2)+16+x^(2)+81=(BD+DC)^(2)}`

`{:\implies \quad \sf 2x^(2)+97=(4+9)^(2)}`

`{:\implies \quad \sf 2x^(2)=169-97}`

`{:\implies \quad \sf 2x^(2)=72}`

`{:\implies \quad \sf x^(2)=36}`

`{:\implies \quad \sf x=√(36)=\boxed{\bf{6}}}`

Hence, Option b) is correct

Pythagoras theorem:- It states that, in a right angled triangle the square of hypotenuse is equal to the sum of the square of base and square of perpendicular