Question

2\frac{1}{2} 6\frac{1}{4} 1\frac{3}{4} a triangle b triangle c

Explanation:

Step1: Assume the triangles are similar

If two triangles are similar, the ratios of their corresponding sides are equal.

Step2: Set up the proportion

Let the height of triangle B be $h_B = 6\frac{1}{4}=\frac{25}{4}$ and base be $b_B = 2\frac{1}{2}=\frac{5}{2}$, the height of triangle C be $h_C=a$ and base be $b_C = 1\frac{3}{4}=\frac{7}{4}$. The proportion is $\frac{h_B}{b_B}=\frac{h_C}{b_C}$, so $\frac{\frac{25}{4}}{\frac{5}{2}}=\frac{a}{\frac{7}{4}}$.

Step3: Simplify the left - hand side of the proportion

$\frac{\frac{25}{4}}{\frac{5}{2}}=\frac{25}{4}\times\frac{2}{5}=\frac{5}{2}$.

Step4: Solve for $a$

We have $\frac{5}{2}=\frac{a}{\frac{7}{4}}$. Cross - multiply gives $2a=\frac{5\times7}{4}=\frac{35}{4}$. Then $a = \frac{35}{8}=4\frac{3}{8}$.

Answer:

$4\frac{3}{8}$