Question

A right-angled triangle has sides (x + 10)

cm, (x + 2) cm and (x + 4) cm. Find the
value of each side of the triangle.
(Hint: Use Pythagoras' theorem. Remem-
ber that the longest side is the hypotenuse)

Answer 1

In a right-angled triangle with sides (x + 10) cm, (x + 2) cm, and (x + 4) cm, we can use Pythagoras' theorem to find the value of each side. By setting up and solving a quadratic equation, we find that the lengths of the sides are 30 cm, 22 cm, and 24 cm.

Step-by-step explanation:

In a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, according to Pythagoras' theorem, we can set up the following equation:

1. (x + 10)2 = (x + 2)2 + (x + 4)2

Expanding and simplifying this equation, we get:

1. x2 + 20x + 100 = x2 + 4x + 4 + x2 + 8x + 16

Combining like terms and further simplifying, we have:

1. x2 - 16x - 120 = 0

Now, we can solve this quadratic equation to find the values of x, which will in turn give us the lengths of the sides:

1. x = -6 or x = 20

Since lengths cannot be negative, the value of x must be 20. Therefore,

1. The length of the side (x + 10) cm = (20 + 10) cm = 30 cm
2. The length of the side (x + 2) cm = (20 + 2) cm = 22 cm
3. The length of the side (x + 4) cm = (20 + 4) cm = 24 cm

So, each side of the right-angled triangle has the lengths 30 cm, 22 cm, and 24 cm, respectively.

Learn more about Pythagoras' theorem