Question

1. a room measures 128\ by 109\. carpeting costs $45.98/m².

a) what is the dimension of the room in inches?
b) what is the area of the room in inches?
c) what is the area of the room in metres?
d) how much will it cost to carpet the room?
e) what is the carpeting cost per square inches?

Explanation:

Part (a)

Step1: Convert feet to inches (12'8'')

Since 1 foot = 12 inches, for 12 feet: \(12\times12 = 144\) inches. Add 8 inches: \(144 + 8 = 152\) inches.

Step2: Convert feet to inches (10'9'')

For 10 feet: \(10\times12 = 120\) inches. Add 9 inches: \(120 + 9 = 129\) inches.

Step1: Recall area formula for rectangle

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

Step2: Substitute the values

Length = 152 inches, Width = 129 inches. So \(A = 152\times129\). Calculate \(152\times129=(150 + 2)\times129=150\times129+2\times129=19350+258 = 19608\) square inches.

Step1: Recall conversion factor (1 inch = 0.0254 meters)

First, find the length and width in meters. Length: \(152\times0.0254\) meters, Width: \(129\times0.0254\) meters.

Step2: Calculate length in meters

\(152\times0.0254 = 3.8608\) meters.

Step3: Calculate width in meters

\(129\times0.0254 = 3.2766\) meters.

Step4: Calculate area in square meters

Area \(A=3.8608\times3.2766\approx12.65\) square meters (rounded to two decimal places).

Answer:

The dimensions of the room are \(152\) inches by \(129\) inches.

Part (b)