Question

What is the area of the rectangle if one side has length of $12{x^3}$ and the other side has a width of $6{x^2}$ ?

Answer 1

Hint: Here we are going to find the area of the rectangle with given length and width using rectangle area formula.
Formula used:
$A = l \times b$
where $A$ is the area, what we are going to find in this problem.
$l$ is the length of the rectangle.
$b$ is the breadth or width of the rectangle.

Complete step-by-step solution:
 Given rectangle if one side has length of $12{x^3}$ and the other side has a width of $6{x^2}$.
We have the formula for finding area of the rectangle, that is,
$A = l \times b$ ----------(1)
where $A$ is the area, what we are going to find in this problem.
$l$ is the length of the rectangle. In this problem we have $12{x^3}$.
$b$ is the breadth or width of the rectangle. In this problem we have $6{x^2}$.
Substitute the values of length and width value in the equation (1), we have
$A = 12{x^3} \times 6{x^2}$
Multiplying the constants and the variables, we get,
$A = \left( {12 \times 6} \right) \times \left( {{x^3} \times {x^2}} \right)$
When we multiply the variables we can use the rule for exponents that is
${a^m} \times {a^n} = {a^{m + n}}$
This gives
$A = 72 \times \left( {{x^{3 + 2}}} \right)$
$A = 72 \times {x^5}$
So finally we have the area of the rectangle with the given length and width,
The final answer is,
$A = 72{x^5}$

Note: The area of the rectangle can be calculated by counting the number of small full squares of dimension $1 \times 1$ sq. units required to cover the rectangle. When multiplying the length by the width always ensure you work in the same units of length. If they are given in different units, change them to the same unit.
In this problem we used the property that the product of powers rule states that when we multiply two powers with the same base, add the exponents.