Question

solve.

1. an auditorium has a floor area of 20,000 square feet. the length of the

auditorium is twice its width. find the dimensions of the room.

Explanation:

Step1: Let the width of the auditorium be \(x\) feet.

Since the length is twice the width, the length is \(2x\) feet.

Step2: Use the area formula for a rectangle \(A = length\times width\).

We know that \(A = 20000\) square feet. Substituting the values of length and width into the formula, we get \(2x\times x=20000\), which simplifies to \(2x^{2}=20000\).

Step3: Solve the equation for \(x\).

Divide both sides of the equation \(2x^{2}=20000\) by \(2\): \(x^{2}=\frac{20000}{2} = 10000\). Then take the square root of both sides: \(x=\sqrt{10000}=100\) (we take the positive value since width cannot be negative).

Step4: Find the length.

Since the length \(l = 2x\), substituting \(x = 100\), we get \(l=2\times100 = 200\) feet.

Answer:

The width of the auditorium is \(100\) feet and the length is \(200\) feet.