Question

which is the closest to the measurement of \overline{ab}?
a 25.5 m
b 5 m
c 18 m
d 11.1 m

Explanation:

Step1: Apply Pythagorean theorem

In rectangle \(ADCB\), \(AD = BC = 15m\), \(DC=AB = 10m\). In right - triangle \(ADB\), by the Pythagorean theorem \(AB^{2}=AD^{2}+DB^{2}\) (where \(DB = DC = 10m\), \(AD = 15m\)). So \(AB=\sqrt{10^{2}+15^{2}}\).

Step2: Calculate the value of \(AB\)

First, calculate \(10^{2}+15^{2}=100 + 225=325\). Then \(\sqrt{325}\approx18.03\) (since \(17^{2}=289\), \(18^{2}=324\), \(19^{2}=361\)).

Answer:

C. \(18m\)