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casey’s den is 10feet longer than it is wide. If the den’s area is 119 square feet, what are the dimensions of the room?
Question
casey’s den is 10feet longer than it is wide. If the den’s area is 119 square feet, what are the dimensions of the room?
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Mathematics
3 years
2021-08-14T16:00:10+00:00
2021-08-14T16:00:10+00:00 1 Answers
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Answers ( )
Answer:
The width is 7ft and the length is 17 ft
Step-by-step explanation:
Let w represent the width of the room and L represents the length of the den.
Given that:
caseys den is 10feet longer than it is wide
Then;
w + 10 = L —- (1)
The area of the den = 119 ft²
Area = w × L
119 = w × L —- (2)
From equation (1);
let w = L – 10.
Now we can replace the value of w into equation (2)
i.e.
(L – 10) × L = 119
L² – 10L – 119 = 0
(L + 7) ( L – 17) = 0
L + 7 = 0 or L – 17 = 0
L = – 7 ft or L = 17 ft
Recall that:
w = L – 10
w = -7 – 10 or w = 17 – 10
w = -17 or w = 7 ft
The area of the den can now be:
Area = -17 ft × – 7ft or 17ft × 7 ft
Area = 119 ft² or 119 ft²
Since it is ideal to use the positive integer,
Then the width is 7ft and the length is 17 ft