Question

the area of a triangular pendant on a necklace is 3/4 square inch. the height of the triangle is 1 1/4 inches. what is the length of the base of the triangle?

Explanation:

Step1: Recall 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 $A = \frac{3}{4}$ square - inch and $h = 1\frac{1}{4}=\frac{5}{4}$ inches.

Step2: Rearrange formula for base

From $A=\frac{1}{2}bh$, we can solve for $b$: $b=\frac{2A}{h}$.

Step3: Substitute values

Substitute $A = \frac{3}{4}$ and $h=\frac{5}{4}$ into the formula for $b$: $b=\frac{2\times\frac{3}{4}}{\frac{5}{4}}$.

Step4: Simplify the expression

First, $2\times\frac{3}{4}=\frac{6}{4}$. Then $\frac{6}{4}\div\frac{5}{4}=\frac{6}{4}\times\frac{4}{5}=\frac{6}{5} = 1\frac{1}{5}$ inches.

Answer:

$1\frac{1}{5}$ inches