The image shows a right-angled triangle ABC, with sides AC = 10 and BC = 4cm. Calculate the length of the…

Question

The image shows a right-angled triangle ABC, with sides AC = 10 and BC = 4cm. Calculate the length of the hypotenuse AB.

ScanSolve AI Tutor · Accepted Answer

To find the length of side AB in the right-angled triangle, we will use the Pythagorean theorem.

Identify the lengths of the two shorter sides (legs) of the right-angled triangle.
The legs are AC and CB.
$AC = 10$
$CB = 4 \text{ cm}$
Apply the Pythagorean theorem, which states that $a^2 + b^2 = c^2$ , where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.
In this case, $a = AC$ , $b = CB$ , and $c = AB$ .
$AC^2 + CB^2 = AB^2$
Substitute the given values into the formula.
$10^2 + 4^2 = AB^2$
Calculate the squares and sum them.
$100 + 16 = AB^2$ $116 = AB^2$
Solve for AB by taking the square root of both sides.
$AB = \sqrt{116}$
Simplify the square root.
We can factor 116 as $4 \times 29$ .
$AB = \sqrt{4 \times 29}$ $AB = \sqrt{4} \times \sqrt{29}$ $AB = 2\sqrt{29} \text{ cm}$
The length of side AB is $2\sqrt{29} \text{ cm}$ .

The image shows a right-angled triangle ABC, with sides AC = 10 and BC = 4cm. Calculate the length of the hypotenuse AB.