Identify the lengths of the two given sides of the right-angled triangle.

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to find the length of the hypotenuse:

Identify the lengths of the two given sides of the right-angled triangle.
Let the two shorter sides (legs) be $a$ and $b$ .
$a = 6 \text{ cm}$ $b = 8 \text{ cm}$
Apply the Pythagorean theorem, which states that for a right-angled triangle, the square of the hypotenuse ( $c$ ) is equal to the sum of the squares of the other two sides ( $a$ and $b$ ).
$a^2 + b^2 = c^2$
Substitute the given values into the formula and calculate.
$6^2 + 8^2 = c^2$ $36 + 64 = c^2$ $100 = c^2$
Solve for $c$ by taking the square root of both sides.
$c = \sqrt{100}$ $c = 10 \text{ cm}$
The length of the hypotenuse is $\mathbf{10 \text{ cm}}$ .

Answer