Question

find the cost of carpeting the following rectangular rooms.
a. dimensions: 7.5 m by 4.5 m; cost = $13.51/m²
b. dimensions: 17 yd by 12 yd; cost = $27/yd²
a. the total cost of carpeting the room is $□.
(type an integer or a decimal. round to the nearest cent as needed.)
b. the total cost of carpeting the room is $□.
(type an integer or a decimal. round to the nearest cent as needed.)

Explanation:

Step1: Calculate the area of the room

The area \(A\) of a rectangle is given by \(A = l\times w\), where \(l\) is the length and \(w\) is the width.
For part a: \(l = 7.5\space m\), \(w=4.5\space m\), so \(A = 7.5\times4.5=33.75\space m^{2}\)
For part b: \(l = 17\space yd\), \(w = 12\space yd\), so \(A=17\times12 = 204\space yd^{2}\)

Step2: Calculate the cost of carpeting

The cost \(C\) is given by \(C=\text{Area}\times\text{Cost per unit area}\)
For part a: \(C = 33.75\times13.51\)

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For part b: \(C=204\times27=(200 + 4)\times27=200\times27+4\times27=5400+108 = 5508\)

Answer:

a. \(455.96\)
b. \(5508\)