Jason builds doghouses for a pet store. Each doghouse is a wooden structure with a rectangular base that has an area of 21 square feet and a length that is 4 feet more than its width.If x represents the width of the doghouse, write an equation in the given form that can be used to determine the possible dimensions of the base of the doghouse.

Let \(x\) be the width of the doghouse in feet. The length of the doghouse is 4 feet more than the width, so the length is \(x + 4\) feet.
The area of the rectangular base is given by:
\[\text { Area} = \text { width} \times \text { length} \]
Substituting the given values:
\[21 = x \times ( x + 4) \]
So, the equation that can be used to determine the possible dimensions of the base of the doghouse is:
\[x( x + 4) = 21\]

Supplemental Knowledge

Quadratic equations are polynomial equations of the form \(ax^ 2 + bx + c = 0\). They often arise in problems involving areas, projectile motion, and optimization. To solve these equations, you can use various methods such as factoring, completing the square, or using the quadratic formula.

From Concepts to Reality

Imagine designing a garden with specific area requirements and shape constraints, then using quadratic equations to accurately find dimensions that satisfy both conditions. Quadratic equations help in this regard!

Understanding quadratic equations is integral for solving real-world issues like designing structures or allocating resources more effectively. If you need assistance in improving your algebra skills or solving particular math issues, UpStudy offers comprehensive tools and resources tailored specifically for you.
For algebra-related queries like this one, try UpStudy’s Algebra Equations Calculator, which can help you solve quadratic equations quickly and accurately.
Join UpStudy today to boost your mathematical prowess and achieve academic excellence!