Question

A rectangular poster has an area of 26 square feet. It is 3 and one fourth
feet wide at its base. What is the height of the​ poster?

Answer 1

To find the height of the rectangular poster, you can use the formula for the area of a rectangle, which is:

\[
\text{Area} = \text{width} \times \text{height}
\]

We know the area is 26 square feet, and the width is given as \(3 \frac{1}{4}\) feet. First, convert \(3 \frac{1}{4}\) to an improper fraction:

\[
3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}
\]

Now, substitute the values into the area formula:

\[
26 = \frac{13}{4} \times \text{height}
\]

To solve for the height, we can isolate it by multiplying both sides by the reciprocal of \(\frac{13}{4}\):

\[
\text{height} = 26 \times \frac{4}{13}
\]

Now perform the multiplication:

\[
\text{height} = \frac{26 \times 4}{13} = \frac{104}{13} = 8
\]

Thus, the height of the poster is:

\[
\text{height} = 8 \text{ feet}
\]