Question: If the sides of a right-angled triangle are (x-2) cm, x cm, (x+2) cm, find the length of each of its side.

Solution:

Given,
Sides of a right-angled triangle are (x-2) cm, x cm, and (x+2) cm.

In a right-angled triangle, the longest side is represented as hypotenuse (h).

Let, (x+2) be h, x be base (b) and (x-2) be perpendicular (p).

Using Pythagoras theorem, we get,
h² = p² + b²
$or, (x +2)² = (x-2)² + x²$
$or, x² + 4x +4 = x² -4x +4 +x²$
$or, x² +4x +4 -x² +4x -4 -x² = 0$
$or, 8x -x² = 0$
$or, x² = 8x$
$or, x × x = 8 ×x$
$\therefore x = 8$

So, x = 8, (x +2) = (8+2) = 10, and (x -2) = (8-2) = 6.

Therefore, the required length of the sides of the given right-angled triangle are 6cm, 8cm and 10cm.

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