Question

The length of the sides of a right triangle are $(2x-1)m,\left(4x\right)m$ and $(4x+1)m$, where $x>0$. Find:
the value of $x$
the area of the triangle.

Answer 1

Since the triangle is right triangle.

Therefore,

${(4x+1)}^2={\left(4x\right)}^2+{(2x-1)}^2$

${\left(4x\right)}^2+1+8x={\left(4x\right)}^2+{\left(2x\right)}^2+1-4x$

$4x^2-12x=0$

$4x(x-3)=0$

$\because x>0\Rightarrow x=3$

Now,

Area of triangle

$=\frac{1}{2}\times \text{base}\times \text{height}=\frac{1}{2}\times (2x-1)\times 4x=2x(2x-1)=(2\times 3)(2\times 3-1)=30m^2$

Hence, this is the answer.