The length of a rectangular picture is 5 inches greater than twice the width. If the perimeter i

The length of a rectangular picture is 5 inches greater than...

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Key Concepts

Properties of Rectangles and Perimeter Formula

Understanding the properties of rectangles is essential in geometry, particularly knowing that a rectangle has opposite sides of equal length and four right angles. The perimeter formula, which is calculated as twice the sum of the length and width, is a key concept used to relate the dimensions of a rectangle to its overall size.

Solving Linear Equations

Solving Linear Equations refers to the process of finding the value of unknown variables in equations where the variable's highest exponent is one. Techniques such as combining like terms, isolating the variable, and using inverse operations are employed to determine solutions systematically.

Algebraic Modeling

Algebraic Modeling involves translating real-world situations or verbal descriptions into algebraic expressions or equations. This approach allows one to represent relationships and constraints mathematically, making complex problems more manageable by using symbolic representations.

Transcript

00:01 So in this problem, we're told that we have a picture that's in the shape of a rectangle.

00:04 And we're told that the length of this rectangle is 5 inches more than twice its width.

00:11 We also know the perimeter is 112 inches.

00:14 We want to find the dimensions.

00:16 So if i draw a rectangle to represent my picture, what don't we know anything about in this case? well, we know nothing about the width.

00:25 So i'm going to call the width w.

00:27 Well, they told us that the length is 5 inches more than twice the width.

00:34 Well, twice the width would mean two times it.

00:37 So if i need to represent 5 inches more than twice the width, that would mean i need to multiply my width by 2 and then add 5.

00:46 So that would mean the length is 2w plus 5.

00:50 Well, now that i have expressions for the length and the width, and i know the perimeter, i can use the perimeter formula to solve for w.

00:59 Well, remember, the perimeter formula is p equals 2l plus 2w.

01:05 So in this case, we know the perimeter is 112, and that's going to be equal to 2 times the length, which we said was 2w plus 5, plus 2 times the width, which we're calling w.

01:21 And we simply need to solve this equation for w.

01:24 So the first thing we're going to do is distribute the 2 .2.

01:27 2 to both terms in the parentheses...

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