Question

solving for side lengths of rectangles
abcd is a rectangle.
use the diagram to answer the questions.
the length of ab is
the length of bc is
the length of ac is

Explanation:

Step1: Properties of a rectangle

In a rectangle, opposite sides are equal. So, \(AB = DC\) and \(BC=AD\). Given \(DC = 12\) and \(AD = 5\), then \(AB = 12\) and \(BC = 5\).

Step2: Using the Pythagorean theorem

For right - triangle \(ABC\) (since \(ABCD\) is a rectangle, \(\angle ABC=90^{\circ}\)), by the Pythagorean theorem \(AC^{2}=AB^{2}+BC^{2}\). Substitute \(AB = 12\) and \(BC = 5\) into the formula: \(AC^{2}=12^{2}+5^{2}=144 + 25=169\). Then \(AC=\sqrt{169}=13\).

Answer:

The length of \(AB\) is \(12\), the length of \(BC\) is \(5\), and the length of \(AC\) is \(13\).