Question

The sides of a right-angled triangle are (x - 1) cm, 3x cm and (3x + 1) cm. Find :

(i) the value of x,

(ii) the lengths of its sides,

(iii) its area.

Answer 1

Longer side = Hypotenuse = (3x + 1) cm
Lengths of other two sides are (x – 1) cm and 3x cm.
Using Pythagoras theorem,
(i)
$(3x+1{)}^2=(x–1{)}^2+(3x{)}^2$
$9x^2+1+6x=x^2+1–2x+9x^2$
$x^2–8x=0$
$x(x–8)=0$
x = 0, 8
But, if x = 0, then one side = 3x = 0, which is not possible.
So, x = 8
(ii)
Thus, the lengths of the sides of the triangle are (x – 1) cm = 7 cm, 3x cm = 24 cm and (3x + 1) cm = 25 cm.
(iii)
Area of the triangle =$\frac{1}{2}\times 7cm\times 24cm=84c{m}^2$