If Mr. Arenth wants to put new carpeting in the room shown, how many square feet should he order?
Given:
\[ L = 14 \text{ ft} \]
\[ W = 6c - 8 \text{ ft} \]
\[ L = 5 + 3c \text{ ft} \]
Calculate the area of the room.
Answer (3)
he should order 140 square feet ; By definition, the area is given by:
A = w ∗ l
Where,
w: width
l: length
We have two expressions for the length:
[ L = 14
L = 5 + 3c ]
Since the length is the same, we equate both expressions:
5 + 3 c = 14
From here, we clear the value of c:
[ 3c = 14 - 5
3c = 9 ]
[ c = \frac{9}{3}
c = 3 ]
Then, we have that the width is given by:
W = 6 c − 8
Substituting the value of c we have:
[ W = 6 (3) -8
W = 18-8
W = 10 ]
Finally, the area is given by:
[ A = w * l
A = 10 * 14
A = 140 ft ^ 2 ]
To find out how many square feet of carpet Mr. Arenth should order, the value for 'c' needs to be known. Once known, the actual dimensions of the room can be calculated, and the area determined by multiplying the length by the width. Without the value of 'c', it is not possible to provide an exact answer. ;
To find the area of the room, the length was given as 14 ft and the width was calculated as 10 ft. Using the area formula, the total area of the room is 140 square feet. Therefore, Mr. Arenth should order 140 square feet of carpeting.
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