Question

what is the distance from the base of the house to the base of the ladder? 5 m 25 m 313 m 17.7 m

Explanation:

Step1: Identify the right - angled triangle

The ladder against the house forms a right - angled triangle, with the ladder as the hypotenuse and the height on the house and the distance from the base of the house to the base of the ladder as the two legs. Let the height on the house be $a = 12$ m and the length of the ladder be $c = 13$ m. We need to find the other leg $b$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Rearranging it to solve for $b$, we get $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values

Substitute $a = 12$ and $c = 13$ into the formula: $b=\sqrt{13^{2}-12^{2}}=\sqrt{(13 + 12)(13 - 12)}=\sqrt{25\times1}=\sqrt{25}=5$ m.

Answer:

5 m