Question

Find the unknown length \[x\]in the following figure:

Answer 1

Hint:Before proceeding further we need to know the statement of Pythagorean theorem.Because to find the value of x,we need to make use of Pythagoras theorem

Statement:In a right angle, the sum of square of base and leg is equal to the sum of the square of the hypotenuse.

Complete step by step solution
${a^2} + {b^2} = {c^2}\,\,\,\,\, \ldots \left( 1 \right)$
Now according to this question we have,
$\begin{gathered}
  a = 6 \\
  b = 8 \\
  c = x \\
\end{gathered} $
Substitute the values in equation\[\left( 1 \right)\], we have,
\[\begin{gathered}
  {\left( 6 \right)^2} + {\left( 8 \right)^2} = {x^2} \\
  36 + 64 = {x^2} \\
  x = \sqrt {100} \\
  x = \pm 10 \\
\end{gathered} \]
Ignore the negative sign as we know that length cannot be negative.
Thus the value of \[x\] is \[10\] .


Note: While writing the roots,\[x = \pm 10\] we must write both the values, later we can ignore one by initially we must write both the values.