Question

self practice
as shown below, in right triangle abc, two robots deliver packages from points a and b to point c.
according to the information on the figure, ac = _m, bc = _m.
my route is 1 m
shorter than yours.
so close!

Explanation:

Step1: Set up variables

Let \( AC = x\) m. Then \( BC=(x - 1)\) m.

Step2: Apply the Pythagorean theorem

In right - triangle \(ABC\), by the Pythagorean theorem \(AB^{2}+AC^{2}=BC^{2}\). Given \(AB = 7\) m, we have \(7^{2}+x^{2}=(x - 1)^{2}\).
Expand \((x - 1)^{2}\) using the formula \((a - b)^{2}=a^{2}-2ab + b^{2}\), so \(49+x^{2}=x^{2}-2x + 1\).

Step3: Solve the equation

Subtract \(x^{2}\) from both sides of the equation:
\(49=-2x + 1\).
Subtract 1 from both sides: \(49-1=-2x\), i.e., \(48=-2x\).
Divide both sides by \(- 2\): \(x=-24\) (rejected) or \(x = 24\).
If \(x = 24\), then \(BC=x - 1=23\).

Answer:

\(AC = 24\) m, \(BC = 23\) m