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Chapter 2: Problem 44

The width of a rectangle is \(4 y^{3}\) units, and the length of the rectangle is \(\frac{13}{2} y^{3}\) units. a) Write an expression for its perimeter. b) Write an expression for its area.

Short Answer

Expert verified
a) The expression for the perimeter is 21\(y^3\) units. b) The expression for the area is 26\(y^6\) square units.

Step by step solution

01

Identify the given expressions for length and width

We are given that the width of the rectangle is \(4y^3\) units, and the length is \(\frac{13}{2}y^3\) units.
02

Use the formula for the perimeter of a rectangle

The formula for the perimeter of a rectangle is given by the formula P = 2 * (length + width). We will plug in the given expressions for the length and width.
03

Calculate the perimeter expression

Now let's plug in the given expressions for the length and width into the perimeter formula: P = 2*(\(\frac{13}{2}y^3 + 4y^3\))
04

Simplify the expression

Now, let's simplify the terms inside the parentheses and then multiply by 2 to obtain the expression for the perimeter: P = 2 * (\(\frac{21}{2}y^3\)) P = 21\(y^3\) So, the expression for the perimeter of the rectangle is 21\(y^3\) units. #b) Write an expression for its area.#
05

Identify the given expressions for length and width (same as part a)

We are given that the width of the rectangle is \(4y^3\) units, and the length is \(\frac{13}{2}y^3\) units.
06

Use the formula for the area of a rectangle

The formula for the area of a rectangle is given by the formula A = length * width. We will plug in the given expressions for the length and width.
07

Calculate the area expression

Now let's plug in the given expressions for the length and width into the area formula: A = \(\frac{13}{2}y^3 * 4y^3\)
08

Simplify the expression

Now, let's simplify the expression by performing multiplication: A = 26\(y^6\) So, the expression for the area of the rectangle is 26\(y^6\) square units.

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