In the diagram, $\triangle A B C$ is right-angled at $B$ with $A B=24$ and $B C=10$. If $A B$ and $B C$ are each increased by 6 , by how much does $A C$ increase?

![](https://cdn.mathpix.com/cropped/2024_04_30_790b6557ee0304df033eg-1.jpg?height=439&width=306&top_left_y=973&top_left_x=969)
Using the Pythagorean Theorem in the given triangle, we obtain

$$
A C=\sqrt{A B^{2}+B C^{2}}=\sqrt{24^{2}+10^{2}}=\sqrt{676}=26
$$

since $A C>0$.

If $A B$ and $B C$ are each increased by 6 , they become 30 and 16 , so the hypotenuse of the new triangle is $\sqrt{30^{2}+16^{2}}=\sqrt{1156}=34$.

Therefore, $A C$ increases by $34-26=8$.

ANSWER: 8