Respuesta :
Answer:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
Explanation:
If two triangles are similar, their corresponding sides are proportional, so we can always use the following equation:
[tex]\frac{A}{B}=\frac{C}{D}[/tex]Therefore, for row (a), we can write the following equation:
[tex]\frac{5\frac{1}{2}}{1\frac{1}{4}}=\frac{2\frac{3}{4}}{D}[/tex]So, changing the mixed number by decimals and solving for D, we get:
[tex]\begin{gathered} \frac{5.5}{1.25}=\frac{2.75}{D} \\ 5.5D=2.75(1.25) \\ 5.5D=3.4375 \\ \frac{5.5D}{5.5}=\frac{3.4375}{5.5} \\ D=0.625 \end{gathered}[/tex]Then, for row (a), D = 0.625 = 5/8
In the same way, we can write and solve the following equation for row (b)
[tex]\begin{gathered} \frac{A}{23.4}=\frac{20.8}{15.6} \\ \frac{A}{23.4}\times23.4=\frac{20.8}{15.6}\times23.4 \\ A=31.2 \end{gathered}[/tex]For row (c), we get:
[tex]\begin{gathered} \frac{12}{B}=\frac{9}{6} \\ 12(6)=9(B) \\ 72=9B \\ \frac{72}{9}=\frac{9B}{9} \\ 8=B \end{gathered}[/tex]For row (d), we get:
[tex]\begin{gathered} \frac{4.5}{3.6}=\frac{C}{2.4} \\ \frac{4.5}{3.6}\times2.4=\frac{C}{2.4}\times2.4 \\ 3=C \end{gathered}[/tex]Therefore, the answers are:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
