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 5 12 13 17

Explanation:

Step1: Recall rectangle properties

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

Step2: Determine side - lengths

Since \(DC = 12\), \(AB=12\). Since \(AD = 5\), \(BC = 5\).

Step3: Use the Pythagorean theorem for the diagonal

In right - triangle \(ABC\) (where \(\angle B = 90^{\circ}\)), by the Pythagorean theorem \(AC^{2}=AB^{2}+BC^{2}\). Substitute \(AB = 12\) and \(BC = 5\): \(AC^{2}=12^{2}+5^{2}=144 + 25=169\), so \(AC=\sqrt{169}=13\).

Answer:

The length of \(AB\) is 12
The length of \(BC\) is 5
The length of \(AC\) is 13