Chapter 7: Q28. (page 460)

The area of a rectangle is $25 x^{2} y^{4}$ square feet. The width of the rectangle is $5 x y$ feet. What is the length of the rectangle?

Short Answer

Expert verified

The length of the rectangle is $5 x y^{3}$ feet.

Step by step solution

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define quotient of power rule.

The quotient of power rule is given by

$\frac{a^{m}}{a^{n}} = a^{m - n}$

Where, $a$ is any non-zero real number and $m > n$ .

Step 3. Define the area of the rectangle.

$Area of the rectangle = length \times width \dots \dots \dots . . (1)$

Step 4. Calculate the length of the given rectangle.

The area of the rectangle $= 25 x^{2} y^{4}$ square feet

The width of the rectangle $= 5 x y$ feet

Let the length of the rectangle $= L$ feet

Use the equation (1).

role="math" localid="1647799427957" $25 x^{2} y^{4} = L \times 5 x y L = \frac{25 x^{2} y^{4}}{5 x y} L = (\frac{25}{5}) (\frac{x^{2}}{x}) (\frac{y^{4}}{y}) L = 5 (\frac{x^{2}}{x}) (\frac{y^{4}}{y})$

Use quotient of power rule.

$L = 5 (x^{2 - 1}) (y^{4 - 1}) L = 5 x y^{3}$

Therefore, the length of the rectangle is $5 x y^{3}$ feet.

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The area of a rectangle is $25 x^{2} y^{4}$ square feet. The width of the rectangle is $5 x y$ feet. What is the length of the rectangle?

Short Answer

Step by step solution

Step 1. Define an expression.

Step 2. Define quotient of power rule.

Step 3. Define the area of the rectangle.

Step 4. Calculate the length of the given rectangle.

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The area of a rectangle is25x2y4 square feet. The width of the rectangle is 5xyfeet. What is the length of the rectangle?

Short Answer

Step by step solution

Step 1. Define an expression.

Step 2. Define quotient of power rule.

Step 3. Define the area of the rectangle.

Step 4. Calculate the length of the given rectangle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Decision Maths

Pure Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

The area of a rectangle is $25 x^{2} y^{4}$ square feet. The width of the rectangle is $5 x y$ feet. What is the length of the rectangle?