Question

1. the area of a rectangle is 1 1/2 square feet. if the height is 2/3 feet, what is the base?

Explanation:

Step1: Convert the mixed number to an improper fraction

The area \(A = 1\frac{1}{2}=\frac{1\times2 + 1}{2}=\frac{3}{2}\) square feet. The formula for the area of a rectangle is \(A=\text{base}\times\text{height}\), let the base be \(b\), and the height \(h=\frac{2}{3}\) feet. So, \(A = b\times h\), which can be rewritten as \(b=\frac{A}{h}\).

Step2: Substitute the values of \(A\) and \(h\) into the formula

We have \(b=\frac{\frac{3}{2}}{\frac{2}{3}}\). When dividing by a fraction, we multiply by its reciprocal. So \(b=\frac{3}{2}\times\frac{3}{2}\).

Step3: Calculate the value of \(b\)

\(\frac{3}{2}\times\frac{3}{2}=\frac{3\times3}{2\times2}=\frac{9}{4} = 2\frac{1}{4}\) feet.

Answer:

The base of the rectangle is \(2\frac{1}{4}\) feet.