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Calculate the length of BC

September 26, 2026Mathematics

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Answer

\text{8 cm}

5 steps

Identify the given information and the relationship between the sides.
The image shows a right-angled triangle $\triangle ABC$ , with the right angle at $B$ (indicated by $AB \perp BC$ ).
We are given:
$AB = 6 \text{ cm}$
$AC = 10 \text{ cm}$ (hypotenuse)
We need to find $BC$ .
Apply the Pythagorean theorem.
For a right-angled triangle, the square of the hypotenuse ( $AC$ ) is equal to the sum of the squares of the other two sides ( $AB$ and $BC$ ).
$AB^2 + BC^2 = AC^2$
Substitute the known values into the equation.
$(6 \text{ cm})^2 + BC^2 = (10 \text{ cm})^2$ $36 \text{ cm}^2 + BC^2 = 100 \text{ cm}^2$
Solve for $BC^2$ .
$BC^2 = 100 \text{ cm}^2 - 36 \text{ cm}^2$ $BC^2 = 64 \text{ cm}^2$
Take the square root to find $BC$ .
$BC = \sqrt{64 \text{ cm}^2}$ $BC = 8 \text{ cm}$
The length of $BC$ is $\boxed{\text{8 cm}}$ .

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