Question

the area of the triangle below is 25/24 square inches. what is the length of the base? express your answer as a fraction in simplest form. 5/6 in

Explanation:

Step1: Recall triangle - area formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $A$ is the area, $b$ is the base, and $h$ is the height. We know that $A = \frac{25}{24}$ square - inches and $h=\frac{5}{6}$ inches.

Step2: Solve for the base $b$

Starting from $A=\frac{1}{2}bh$, we can isolate $b$. First, multiply both sides of the equation by $2$ to get $2A = bh$. Then, divide both sides by $h$: $b=\frac{2A}{h}$.
Substitute $A=\frac{25}{24}$ and $h = \frac{5}{6}$ into the formula for $b$:
\[

$$\begin{align*} b&=\frac{2\times\frac{25}{24}}{\frac{5}{6}}\\ &=\frac{\frac{25}{12}}{\frac{5}{6}}\\ &=\frac{25}{12}\times\frac{6}{5}\\ &=\frac{25\times6}{12\times5}\\ &=\frac{150}{60}\\ &=\frac{5}{2} \end{align*}$$

\]

Answer:

$\frac{5}{2}$ in