Q51. - Algebra 1

Question

The parking lot shown is to be paved. What is the area to be paved?

Step-by-Step Solution

Answer

The area of the parking lot to be paved is $\left(10x^2+7x-12\right)$ units².

Step 1. Define an expression.

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

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where, $a$ is any non-zero real number.

Step 3. Define the area of the rectangle.

Area of the rectangle $\left(A\right)=$ length $\times$width ……….. (1)

A = 10 x 2 + 15 x − 8 x − 12 A = 10 x 2 + 7 x − 12 Step 4. Calculate the area of the parking lot to be paved.

Observe the figure.

The shape of the parking lot is like a rectangle.

The length of the parking lot units

The width of the parking lot units

Use the equation (1).

The area of the parking lot to be paved is

$\begin{array}{c}A=\left(5x-4\right)\left(2x+3\right)\\ A=5x\left(2x+3\right)-4\left(2x+3\right)\\ A=5x\left(2x\right)+5x\left(3\right)-4\left(2x\right)-4\left(3\right)\end{array}$

Use the power of a product rule.

Therefore, the area of the parking lot to be paved is $10x^2+7x-12$ units².