Question

the rectangle below has an area of $35x^{3}$ square meters and a width of $5x$ meters. what is the length of the rectangle? length $5x$ $35x^{3}$ length = meters

Explanation:

Step1: Recall the formula for the area of a rectangle

The area of a rectangle is \(A = \text{length}\times\text{width}\). So, \(\text{length}=\frac{A}{\text{width}}\).

Step2: Substitute the given values into the formula

Given \(A = 35x^{3}\) and \(\text{width}=5x\). Then \(\text{length}=\frac{35x^{3}}{5x}\).

Step3: Simplify the expression

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\) and \(\frac{35}{5}=7\), \(\frac{x^{3}}{x}=x^{3-1}=x^{2}\). So \(\frac{35x^{3}}{5x}=7x^{2}\).

Answer:

\(7x^{2}\) meters