Question

The lengths of the sides of a right triangle are $5x+2$, $5x$ and $3x-1$.

If $x>0$ then the length of each side is?

• A. $17,15,8$
• B. $17,15,9$
• C. $18,15,10$
• D. $20,5,12$

Answer 1

Answer: (A)

$17,15,8$

Sides of triangle are $5x+2,5x$ and $3x-5$

As $x>0$ so the longest side or the hypotenuse is $5x+2$

Using pythagoras theorem

${(3x-1)}^2+{\left(5x\right)}^2={(5x+2)}^2\Rightarrow 9x^2+1-6x+{25x}^2=25x^2+4+20x\Rightarrow 9x^2-26x-3=0\Rightarrow 9x^2-27x+x-3=0\Rightarrow 9x(x-3)+1(x-3)=0\Rightarrow (9x+1)(x-3)=0\Rightarrow x=-\frac{1}{9},3$

But $x>0$

$\Rightarrow x=3$

So the sides are

$5x+2=15+2=175x=153x-1=9-1=8$