Question

The hypotenuse of a right-angled triangle is 20 metres. If the difference between the length of the other sides be 4 metres, find the other sides.

Answer 1

Let one side of the right-angled triangle be $x$ m and the other side be $\left(x+4\right)$ m.
On applying Pythagoras theorem, we have:

$$\begin{gathered} {20}^2={(x+4)}^2+x^2 \\ \Rightarrow 400=x^2+8x+16+x^2 \\ \Rightarrow 2x^2+8x-384=0 \\ \Rightarrow x^2+4x-192=0 \\ \Rightarrow x^2+(16-12)x-192=0 \\ \Rightarrow x^2+16x-12x-192=0 \\ \Rightarrow x(x+16)-12(x+16)=0 \\ \Rightarrow (x+16)(x-12)=0 \\ \Rightarrow x=-16\text{or}x=12 \end{gathered}$$

The value of x cannot be negative.
Therefore, the base is 12 m and the other side is {(12 + 4) = 16 m}.