Chapter E, Problem 8.12EX

To determine

To find the value of $x$ , the sides of triangle with sides of lengths $x$ , $x+7$ and $x+8$ is a right angle triangle.

Answer to Problem 8.12EX

Option (b)

Explanation of Solution

Given information: The length of the sides of the right triangle are $x$ , $x+7$ and $x+8$ .

Concept used:

For right angles triangle, $B^2+P^2=H^2$

where, P, B and H be the perpendicular, base and hypotenuse of right angled triangle.

  $\begin{array}{l}$ x^2+{(x+7)}^2={(x+8)}^2$x^2+x^2+49+14x=x^2+64+16x\\ x^2-2x-15=0\\ x^2-5x+3x-15=0\\ x(x-5)+3(x-5)=0\\ (x-5)(x+3)=0\\ x=5;x\ne -3\end{array}$

Hence, the value of $x$ is 5.