Given:
• c = 20
,
• h = 15
,
• j = 12
,
• k = 16
Let's find the measures of the mssing sides if triangle ABC is similar to triangle JKH.
Here, the missing sides are:
Side a and Side b
Since both triangles are similar, the corresponding sides will be proportional.
To solve for the length of side a, apply the proportionality equation:
[tex]\frac{c}{h}=\frac{a}{j}[/tex]
Plug in values and solve for a:
[tex]\begin{gathered} \frac{20}{15}=\frac{a}{12} \\ \\ \text{ Cross multiply:} \\ 15a=20*12 \\ \\ 15a=240 \\ \text{ } \\ \text{ Divide both sides by 15:} \\ \frac{15a}{15}=\frac{240}{15} \\ \\ a=16 \end{gathered}[/tex]
Thereofore, the length of side a = 16
To solve for the length of side b, apply the equation:
[tex]\frac{c}{h}=\frac{b}{k}[/tex]
Plug in the values for the variables and solve for b:
[tex]\begin{gathered} \frac{20}{15}=\frac{b}{16} \\ \\ 15b=20*16 \\ \\ 15b=320 \\ \\ b=\frac{320}{15} \\ \\ b=21.3 \end{gathered}[/tex]
The length of b is 21.3
ANSWER:
• a = 16
,
• b = 21.3
