Q28. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

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.

$\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{rectangle}=\mathrm{length}\times \mathrm{width} \dots \dots \dots .. \left(1\right)$

Step 4. Calculate the length of the given rectangle.

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

The width of the rectangle $=5xy$ feet

Let the length of the rectangle $=L$ feet

Use the equation (1).

$$\begin{gathered} 25x^2{y}^4=L\times 5xy \\ L=\frac{25x^2{y}^4}{5xy} \\ L=\left(\frac{25}{5}\right)\left(\frac{x^2}{x}\right)\left(\frac{y^4}{y}\right) \\ L=5\left(\frac{x^2}{x}\right)\left(\frac{y^4}{y}\right) \end{gathered}$$

Use quotient of power rule.

$$\begin{gathered} L=5\left(x^{2-1}\right)\left(y^{4-1}\right) \\ L=5x{y}^3 \end{gathered}$$

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