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A rectangular kitchen is 8 feet longer than it is wide. Its area is 240 square feet. How long, in feet, is it?
- a)12
- b)16
- c)20
- d)24
- e)30
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A rectangular kitchen is 8 feet longer than it is wide. Its area is 24...
The correct answer is c.
A rectangular kitchen that is 8 feet longer than it is wide with width w would have length l = w + 8, or w = l - 8.
Since the area A = 240 = Iw, substitute w = l - 8 into 240 = Iw to get 240 = l(l - 8) = l2 - 8l, or l2 - 8l - 240 = 0.
To find l, factor l2 - 8l - 240 = 0 into (l + 12)(l — 20) = 0.
Thus l = -12 (which doesn’t make sense because a kitchen cannot have a negative length), or l = 20.
A rectangular kitchen that is 8 feet longer than it is wide with width w would have length l = w + 8, or w = l - 8.
Since the area A = 240 = Iw, substitute w = l - 8 into 240 = Iw to get 240 = l(l - 8) = l2 - 8l, or l2 - 8l - 240 = 0.
To find l, factor l2 - 8l - 240 = 0 into (l + 12)(l — 20) = 0.
Thus l = -12 (which doesn’t make sense because a kitchen cannot have a negative length), or l = 20.
Most Upvoted Answer
A rectangular kitchen is 8 feet longer than it is wide. Its area is 24...
Solution:
Let's assume that the width of the rectangular kitchen is x feet. According to the given information, the length of the rectangular kitchen is 8 feet longer than its width, so the length would be x + 8 feet.
The area of a rectangle is calculated by multiplying its length and width. Therefore, we have the equation:
Area = Length × Width
Substituting the given values, we get:
240 = (x + 8) × x
Simplifying the equation, we have:
240 = x^2 + 8x
Rearranging the equation to form a quadratic equation, we get:
x^2 + 8x - 240 = 0
Now, we can solve this quadratic equation to find the value of x, which represents the width of the rectangular kitchen.
Factoring the quadratic equation, we have:
(x + 20)(x - 12) = 0
Setting each factor equal to zero and solving for x, we get:
x + 20 = 0 or x - 12 = 0
x = -20 or x = 12
Since the width cannot be negative, we discard the solution x = -20.
Therefore, the width of the rectangular kitchen is x = 12 feet.
Finally, we can find the length of the kitchen by adding 8 to the width:
Length = 12 + 8 = 20 feet
Hence, the length of the rectangular kitchen is 20 feet, which is the correct answer according to option C.
Let's assume that the width of the rectangular kitchen is x feet. According to the given information, the length of the rectangular kitchen is 8 feet longer than its width, so the length would be x + 8 feet.
The area of a rectangle is calculated by multiplying its length and width. Therefore, we have the equation:
Area = Length × Width
Substituting the given values, we get:
240 = (x + 8) × x
Simplifying the equation, we have:
240 = x^2 + 8x
Rearranging the equation to form a quadratic equation, we get:
x^2 + 8x - 240 = 0
Now, we can solve this quadratic equation to find the value of x, which represents the width of the rectangular kitchen.
Factoring the quadratic equation, we have:
(x + 20)(x - 12) = 0
Setting each factor equal to zero and solving for x, we get:
x + 20 = 0 or x - 12 = 0
x = -20 or x = 12
Since the width cannot be negative, we discard the solution x = -20.
Therefore, the width of the rectangular kitchen is x = 12 feet.
Finally, we can find the length of the kitchen by adding 8 to the width:
Length = 12 + 8 = 20 feet
Hence, the length of the rectangular kitchen is 20 feet, which is the correct answer according to option C.
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A rectangular kitchen is 8 feet longer than it is wide. Its area is 240 square feet. How long, in feet, is it?a)12b)16c)20d)24e)30Correct answer is option 'C'. Can you explain this answer?
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