Question

find the measure of $overline{bc}$. assume that the given figure is not drawn to scale. a 2$\frac{3}{4}$ in. b c 6 in. o a) 2$\frac{1}{4}$ in. o b) 3$\frac{1}{4}$ in. o c) $\frac{1}{2}$ in. o d) $\frac{1}{5}$ in.

Explanation:

Step1: Identify total length and part - length

The total length $AC = 6$ in and the length of $AB=2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}$ in.

Step2: Calculate length of $BC$

We know that $AC=AB + BC$, so $BC=AC - AB$. Substitute the values: $BC = 6-\frac{11}{4}=\frac{6\times4}{4}-\frac{11}{4}=\frac{24 - 11}{4}=\frac{13}{4}=3\frac{1}{4}$ in.

Answer:

B. $3\frac{1}{4}$ in.