a rectangular bedroom is 7 feet longer than its width. Its area is 228 feet^2. what is the width of the room?
A bedroom is 7 feet longer than its width.
This mean
L = 7 + W
A = L * W = 228
( 7 + W ) * W = 228
7 W + W ^ 2 = 228
W ^ 2 + 7 W = 228 Subtract 228 to both sides
W ^ 2 + 7 W - 228 = 228 - 228
W ^ 2 + 7 W - 228 = 0
The solutions are :
W = 12 and W = - 19
Width can't be negative so W = 12 ft
L = 7 + W = 7 + 12 = 19 ft
A = L * W = 19 * 12 = 228 ft ^ 2
thank you so much Bosnian.. :-)
Ah, the mysterious rectangular bedroom, hiding its dimensions like a secret! Well, fear not, my friend, for I shall reveal the answer with a sprinkle of humor.
Let's call the width of the room "W." According to the information given, the length of the room is 7 feet longer than the width, meaning it is W + 7.
Now, we know that the area of a rectangle is the product of its length and width. So, by multiplying the length and width, we should get an area of 228 square feet.
(W + 7) * W = 228
Now, let's solve this equation to find the width of the room:
W² + 7W = 228
Hmm, this equation is not very fun, is it? Let's bring in some clowns to help us out!
🤡🤡🤡
Now, let's pretend that the clowns will juggle the numbers for us! Oh, look! They've magically simplified the equation for us:
W² + 7W - 228 = 0
Now we can use the quadratic formula to solve for W, but let me tell you, quadratic formulas are not the funniest jokes in the world. So, instead, let's do a little bit of magic!
Ala-kazam! 🔮
After some magical calculations, the width of the room reveals itself: W = 12 feet!
Ta-da! The width of the room is 12 feet! Now you can plan your furniture placement and turn that rectangle into a magical space! 🎉
To find the width of the rectangular bedroom, we can set up an equation based on the given information.
Let's assume the width of the room is represented by "W" (in feet).
According to the given information, the length of the room is 7 feet longer than its width, so the length can be represented as "W + 7" (in feet).
The formula for the area of a rectangle is length multiplied by width. Therefore, the area of the bedroom can be expressed as:
Area = Length * Width
In this case, the area is given as 228 square feet, so we have:
228 = (W + 7) * W
Now, we can solve this equation to find the width of the room.
Expanding the equation, we have:
228 = W^2 + 7W
Rearranging the equation, we get:
W^2 + 7W - 228 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula.
Factoring the equation, we find:
(W - 12)(W + 19) = 0
From this equation, we have two possible solutions: W = 12 or W = -19. However, the width cannot be negative, so the only valid solution is W = 12.
Therefore, the width of the room is 12 feet.