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Question
The sides of a right-angled triangle are (x – 1) cm, 3x cm and (3x + 1) cm. Find:
- the value of x,
- the lengths of its sides,
- its area.
Solution
Longer side = Hypotenuse = (3x + 1) cm
Lengths of other two sides are (x – 1) cm and 3x cm.
Using Pythagoras theorem,
(3x + 1)2 = (x – 1)2 + (3x)2
9x2 + 1 + 6x = x2 + 1 – 2x + 9x2
x2 – 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
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.
Area of the triangle = `1/2` × 7 cm × 24 cm = 84 cm2
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