The length of a rectangle is 3 feet longer than the width....

The length of a rectangle is 3 feet longer than the width. The perimeter is 30 feet. Find the dimensions of the rectangle.
a. length $=8$ feet; width $=5$ feet
b. length $=8$ feet; width $=7$ feet
c. length $=9$ feet; width $=6$ feet

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Properties of Rectangles

Rectangles are quadrilaterals with four right angles and opposite sides that are equal in length. Understanding these properties is essential because they allow one to accurately apply formulas for calculating various measurements, such as perimeter and area.

Perimeter Formula

The perimeter of a rectangle is calculated by adding twice the length and twice the width (P = 2 × (length + width)). This formula is a basic geometric principle that connects the shape's dimensions in a linear equation.

Algebraic Representation of Relationships

Translating word problems into algebraic expressions involves representing unknown quantities with variables. When one dimension is described in relation to another, such as being a fixed amount longer, this concept is crucial to set up the appropriate equations.

Solving Linear Equations

Solving linear equations entails combining like terms and isolating the variable to determine its value. This process is fundamental in algebra, allowing one to find specific numerical solutions that satisfy the conditions established by a problem.

Transcript

00:01 For problem number one, we want to find the length of a rectangle that is three feet longer than the width, that also has a perimeter of 30 feet.

00:10 We have three choices here, options a, b, and c that can fit these parameters.

00:16 So let's first write two equations, let's make a system of equations, to represent this rectangle.

00:22 I first want to work with the length of a rectangle is three feet longer than the width.

00:28 So i know it's going to end up equaling l, since that's our length.

00:33 And since our length is three feet longer than our width, i'm going to want to add three feet onto our width.

00:44 So that is our first equation.

00:46 Our second equation has to deal with the perimeter of a triangle.

00:51 Since perimeter is 30 feet, i know that's going to be our total.

00:57 In order to find the perimeter of a rectangle, i need to add up all the sides.

01:05 Since i know there's two lengths and two widths, i'm going to do two times l plus two times w to get my perimeter.

01:18 And now this is my second equation.

01:22 What i want to do next is check and see whether a, b, or c fits into these equations.

01:29 So i'm going to take each one and plug it into each equation to see to see.

01:34 See if it works.

01:37 So first i want to plug in 8 equals 3 plus 5...

Please give Ace some feedback