Question

kite abcd represents a softball field that is being built. if ac = 48 meters, what is the perimeter of the field? 40 meters 70 meters 140 meters 218 meters

Explanation:

Step1: Find the length of \(AB\)

In right - triangle \(ABC\), \(AC = 48\) meters, half of \(AC\) is \(24\) meters (\(AC\) is bisected by the other diagonal in a kite), and \(BO=18\) meters (\(O\) is the intersection of the diagonals). Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), for \(\triangle ABO\), \(AB=\sqrt{24^{2}+18^{2}}=\sqrt{576 + 324}=\sqrt{900}=30\) meters.

Step2: Find the length of \(AD\)

In right - triangle \(ADC\), half of \(AC\) is \(24\) meters, and \(DO = 32\) meters. Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), for \(\triangle ADO\), \(AD=\sqrt{24^{2}+32^{2}}=\sqrt{576+1024}=\sqrt{1600} = 40\) meters.

Step3: Calculate the perimeter of the kite

Since a kite has two pairs of adjacent equal sides, \(AB = BC\) and \(AD=DC\). The perimeter \(P=2(AB + AD)\). Substituting \(AB = 30\) meters and \(AD = 40\) meters, \(P=2(30 + 40)=2\times70=140\) meters.

Answer:

140 meters