Question

A poster has an area of 10 square feet. Its perimeter is 14 feet. What are the dimensions of the poster?

feet by
feet

Answer 1

To find the dimensions of the poster, we can set up a system of equations based on the area and the perimeter.

Let:
- \( l \) = length of the poster
- \( w \) = width of the poster

From the problem, we have the following information:

1. Area:
\[
l \cdot w = 10
\]

2. Perimeter:
\[
2l + 2w = 14
\]
Dividing the perimeter equation by 2 gives:
\[
l + w = 7
\]

Now we can solve this system of equations. From the second equation, we can express \( l \) in terms of \( w \):
\[
l = 7 - w
\]

Now substitute \( l \) into the area equation:
\[
(7 - w) w = 10
\]

Expanding this gives:
\[
7w - w^2 = 10
\]
Rearranging into a standard quadratic equation:
\[
w^2 - 7w + 10 = 0
\]

Next, we can factor or use the quadratic formula to solve for \( w \). The equation factors nicely:
\[
(w - 5)(w - 2) = 0
\]

This gives us:
\[
w = 5 \quad \text{or} \quad w = 2
\]

Using \( w = 5 \):
\[
l = 7 - 5 = 2
\]

Using \( w = 2 \):
\[
l = 7 - 2 = 5
\]

Thus, the dimensions of the poster are:
\[
\boxed{5} \text{ feet by } \boxed{2} \text{ feet}
\]