Answer:
The height of the triangle is 3 inches.
Explanation:
Given:
[tex]\begin{gathered} \text{Base of the triangle}=3\frac{2}{5}\text{ inches} \\ \text{Area of the triangle}=5\frac{1}{10}\text{ inches} \end{gathered}[/tex]
We change the mixed fractions to improper fractions below:
[tex]\begin{gathered} \text{Base of the triangle}=3\frac{2}{5}=\frac{(5\times3)+2}{5}=\frac{17}{5}\text{ inches} \\ \text{Area of the triangle}=5\frac{1}{10}=\frac{(10\times5)+1}{10}=\frac{51}{10}\text{ inches} \end{gathered}[/tex]
We want to find the height of the triangle.
Recall that the area of a triangle is calculated using the formula below.
[tex]\text{Area}=\frac{1}{2}\times\text{Base}\times Height[/tex]
Substitute the given values:
[tex]\frac{51}{10}=\frac{1}{2}\times\frac{17}{5}\times\text{Height}[/tex]
Multiply the numerators and denominators on the right side of the equation.
[tex]\begin{gathered} \frac{51}{10}=\frac{1\times17}{2\times5}\times\text{Height} \\ \frac{51}{10}=\frac{17\times\text{Height}}{10} \end{gathered}[/tex]
Multiply both sides by 10.
[tex]\begin{gathered} \frac{51}{10}\times10=\frac{17\times\text{Height}}{10}\times10 \\ \implies51=17\times\text{Height} \end{gathered}[/tex]
To solve for the height, divide both sides by 17.
[tex]\begin{gathered} \frac{51}{17}=\frac{17\times\text{Height}}{17} \\ 3=\text{Height} \\ \text{Height = 3 inches} \end{gathered}[/tex]
The height of the triangle is 3 inches.
