Question

1. the area of the rectangle is $10\frac{5}{6}\text{ in}^2$. what is the length of the base?

$4\frac{1}{3}\text{ in}$
formula:
plug in values:
b
base:

Explanation:

Step1: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \) (or in this case, \( A = b \times h \), where \( b \) is the base and \( h \) is the height). So the formula is \( A = b \times h \).

Step2: Plug in the given values

We know that \( A = 10\frac{5}{6} \) in² and \( h = 4\frac{1}{3} \) in. First, convert the mixed numbers to improper fractions. \( 10\frac{5}{6}=\frac{10\times6 + 5}{6}=\frac{65}{6} \) and \( 4\frac{1}{3}=\frac{4\times3+1}{3}=\frac{13}{3} \). So plugging into the formula \( A = b\times h \), we get \( \frac{65}{6}=b\times\frac{13}{3} \).

Step3: Solve for \( b \)

To solve for \( b \), we can divide both sides of the equation by \( \frac{13}{3} \), which is the same as multiplying by its reciprocal \( \frac{3}{13} \). So \( b=\frac{65}{6}\times\frac{3}{13} \). Simplify the fractions: \( 65\) and \( 13 \) have a common factor of \( 13 \) (since \( 65\div13 = 5 \)) and \( 6 \) and \( 3 \) have a common factor of \( 3 \) (since \( 6\div3=2 \)). So \( b=\frac{5}{2}\times\frac{1}{1}=\frac{5}{2}=2\frac{1}{2} \) in.

Formula:

\( A = b \times h \) (where \( A \) is the area, \( b \) is the base, and \( h \) is the height of the rectangle)

Plug in Values:

\( 10\frac{5}{6}=b\times4\frac{1}{3} \) (or in improper fractions \( \frac{65}{6}=b\times\frac{13}{3} \))

Base:

\( 2\frac{1}{2} \) inches (or \( \frac{5}{2} \) inches)

Answer:

Formula: \( A = b \times h \)
Plug in Values: \( 10\frac{5}{6}=b\times4\frac{1}{3} \)
Base: \( 2\frac{1}{2} \) in