Question

Find the length of the third side. If necessary, round to the nearest tenth. 10 24

Answer 1

26 units

Explanation:

To find the missing side length, we need to use Pythagoras theorem, as this triangle is a right triangle.

Formula: h² = x² + y² [h = hypotenuse, x and y = legs]

Legs: 10 units and 24 units (Stated in comments)

Finding the third side of the triangle (h):

⇒ h² = 10² + 24²

Simplify the LHS:

⇒ h² = 100 + 576

⇒ h² = 676

Take a square root both sides:

⇒ √h² = √676

⇒ h = ±26

⇒ h = 26 (Side lengths can never be negative)

Thus, the length of the third side is 26 units.

Answer 2

26 units

Explanation:

Pythagoras' Theorem:
`\sf a^2+b^2=c^2`

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given

• a = 10
• b = 24

Substitute the given values into the formula and solve for c:

`\sf \implies 10^2+24^2=c^2`

`\sf \implies c^2=676`

`\sf \implies c=\pm√(676)`

`\sf \implies c=\pm26`

Since length is positive, c = 26 only