Question

problems: substituting values in formulas

1. the area of a triangle is equal to $\frac{1}{2}$ times the base times the height: $a = \frac{1}{2}bh$. determine $h$ when $a = 3\frac{1}{2}$ square feet and $b = 1\frac{3}{4}$ feet.

Explanation:

Step1: Convert mixed - numbers to improper fractions

$A = 3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}$ square feet, $b = 1\frac{3}{4}=\frac{1\times4+3}{4}=\frac{7}{4}$ feet.

Step2: Rearrange the area formula for $h$

Starting with $A=\frac{1}{2}bh$, we can solve for $h$ by multiplying both sides by $2$ and then dividing by $b$. So $h=\frac{2A}{b}$.

Step3: Substitute the values of $A$ and $b$ into the formula for $h$

$h=\frac{2\times\frac{7}{2}}{\frac{7}{4}}$. First, $2\times\frac{7}{2}=7$. Then $h = 7\div\frac{7}{4}$.

Step4: Divide by a fraction

Dividing by a fraction is the same as multiplying by its reciprocal. So $h = 7\times\frac{4}{7}=4$ feet.

Answer:

$4$ feet