Question

In a right-angled triangle, the measures of the perpendicular sides are 6 cm and 11 cm. Find the length of the third side.

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Answer 1

In a right-angled triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's denote the length of the hypotenuse as "c" and the lengths of the perpendicular sides as "a" and "b."

According to the Pythagorean theorem:

c² = a² + b²

Given:

Length of one perpendicular side (a) = 6 cm

Length of the other perpendicular side (b) = 11 cm

Now, plug in the given values and solve for the length of the hypotenuse (c):

c² = 6² + 11²

c² = 36 + 121

c² = 157

Take the square root of both sides to find the length of the hypotenuse (c):

c = √157

c ≈ 12.53 cm

Therefore, the length of the third side (hypotenuse) of the right-angled triangle is approximately 12.53 centimeters.

Answer 2

Length of third side = 12.53 cm

Explanation:

Given that in a right-angled triangle, the measures of the perpendicular sides are 6 cm and 11 cm.

Let the third side be 'x'.

We can apply the Pythagoras theorem to calculate the length of the third side.

Pythagoras theorem:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case,

• The hypotenuse is the third side, which is 'x'.
• The other two sides are 6 cm and 11 cm.

By using Pythagoras theorem, We can say that

`\sf x^2= 6^2 + 11^2`

`\sf x^2 = 36 + 121`

`\sf x^2 = 157`

`\sf x = √(157)`

`\sf x \approx 12.53 \textsf{ in 2 d.p.}`

Therefore, the length of the third side of the right-angled triangle is 12.53cm.