Question

The length of the sides of a right triangle are $5x+2,5xand3x-1$ find the length of each side .

Answer 1

Consider the given sides of right angle $5x+2,5x,3x-1$

Using the Pythagoras theorem

${(5x+2)}^2={\left(5x\right)}^2+{(3x-1)}^2$

$25x^2+4+20x=25x^2+9x^2+1^1-6x$

$-9x^2+26x+3=0$

$9x^2-26x-3=0$

$9x^2-27x+x-3=0$

$9x(x-3)+1(x-3)=0$

$(x-3)(9x+1)=0$

When,

$9x+1=0$

$x=\frac{-1}{9}$

It is a negative value. so ignore it

When,$x-3=0$

Then $x=3$

Put $x=3$ in these given sides$5x+2,5x,3x-1$, we get

$5\times 3+2,5\times 3,3\times 3-1$

$17,15,8$

Hence these are the required value of sides of right angle triangle